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arxiv: 2602.06606 · v2 · submitted 2026-02-06 · 🧬 q-bio.PE · math.DS

Multiple timescales in collective motion: daily and intraday upstream fish migration focusing on Feller condition

Hidekazu Yoshioka This is my paper

Pith reviewed 2026-05-16 06:50 UTC · model grok-4.3

classification 🧬 q-bio.PE math.DS
keywords fish migrationdiffusion bridgesFeller conditionstochastic differential equationscollective motionAyutimescalesintermittency
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The pith

Daily fish migration is less randomized and intermittent than intraday migration according to the Feller condition on diffusion bridges.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper models upstream fish migration using diffusion bridges, nonlinear stochastic differential equations pinned at both initial and terminal conditions. Drift and diffusion coefficients come from time-dependent average and variance curves fitted directly to fish count data, which also guarantees unique solutions exist. Sample paths of these bridges exhibit qualitatively different behaviors depending on the Feller condition, the ratio of diffusion size to drift size. When applied to juvenile Ayu upstream migration counts in Japan, the daily data and intraday data yield distinct Feller indices, with daily paths appearing less randomized and intermittent. The work concludes that the Feller condition offers a practical way to compare and evaluate migration phenomena across multiple timescales.

Core claim

Application to juvenile upstream migration of Plecoglossus altivelis altivelis shows that daily and intraday fish count data correspond to distinctive Feller indices, showing that the former is qualitatively less randomized and intermittent. Diffusion bridges are built from nonlinear SDEs whose drift and diffusion coefficients are fixed by the fitted time-dependent parameterized average and variance curves, with unique existence of solutions rigorously guaranteed; sample paths then differ in qualitative properties according to the ratio between the sizes of diffusion and drift.

What carries the argument

Diffusion bridges from nonlinear SDEs with pinned ends, whose drift and diffusion coefficients are set by time-dependent parameterized average and variance curves fitted to fish count data; the Feller condition (ratio of diffusion size to drift size) controls qualitative path properties such as intermittency.

If this is right

  • Daily-scale migration paths are less intermittent and less likely to exhibit extreme fluctuations than intraday paths under the fitted models.
  • The Feller condition serves as an effective quantitative tool for evaluating and comparing fish migration across daily and intraday timescales.
  • Unique existence of solutions is guaranteed for the constructed diffusion bridges at both timescales.
  • Similarities and differences between daily and intraday Ayu migration can be clarified by comparing their respective Feller indices.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same diffusion-bridge construction could be tested on other migratory species to check whether distinct Feller indices appear consistently across timescales.
  • If Feller indices reliably separate short-term and long-term collective motion, the approach might help forecast how environmental changes affect migration at each scale.
  • Conservation planning for Ayu could incorporate separate models for daily versus intraday movement to improve timing of habitat interventions.
  • Extending the fitting procedure to include environmental covariates would test whether the Feller indices remain stable or shift under varying river conditions.

Load-bearing premise

The time-dependent parameterized average and variance curves fitted to fish count data correctly capture the true drift and diffusion coefficients of the underlying migration process.

What would settle it

New fish count data that produce similar Feller indices for both daily and intraday scales, or numerical simulations of the fitted bridges that fail to show the predicted difference in path intermittency and randomization.

Figures

Figures reproduced from arXiv: 2602.06606 by Hidekazu Yoshioka.

Figure 1
Figure 1. Figure 1: Functional shapes of , (1 ) m n t m n f c t t =− ( , , , 0 m n cmn  ) with mn, c chosen so that 01 max 1 t t f  = . Values of (mn, ) are Black: (0.5,0.5) , Red: (5,10) , Green: (10,5) , and Blue: (10,10) . For the models using real data, see Section 3 [PITH_FULL_IMAGE:figures/full_fig_p008_1.png] view at source ↗
Figure 8
Figure 8. Figure 8: Comparison between empirical (circles) and fitted (curves) autocorrelation functions (ACF): (a) daily case (b) intraday case. Colors represent the results for t = 0.01 (red), t = 0.36 (green), and t = 0.72 (blue) [PITH_FULL_IMAGE:figures/full_fig_p019_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Comparison of the Feller indices F between daily (red) and intraday (blue) cases on an ordinary logarithmic scale [PITH_FULL_IMAGE:figures/full_fig_p019_9.png] view at source ↗
read the original abstract

Fish migration is a collective phenomenon that has multiple timescales, ranging from daily to intraday (hourly or even finer). We propose a unified mathematical approach using diffusion bridges, nonlinear stochastic differential equations with pinned initial and terminal conditions, to model both daily and intraday fish migration phenomena. Drift and diffusion coefficients of these bridges are determined based on time-dependent parameterized average and variance curves fitted against fish count data, with which the unique existence of their solutions is rigorously guaranteed. We show that sample paths of the diffusion bridges have qualitatively distinctive properties depending on the Feller condition, namely, the ratio between the sizes of diffusion and drift. Our application study about the juvenile upstream migration of Plecoglossus altivelis altivelis (Ayu) in Japan clarifies similarities and differences between daily and intraday migration phenomena. Particularly, we discuss that the daily and intraday fish count data correspond to distinctive Feller indices, showing that the former is qualitatively less randomized and intermittent. The results obtained in this study suggest that the Feller condition potentially serves as an effective tool for evaluating fish migration phenomena of Ayu across different timescales.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript proposes a unified framework using diffusion bridges constructed from nonlinear SDEs whose drift and diffusion coefficients are obtained from time-dependent parameterized average and variance curves fitted to fish-count data. It asserts that the Feller condition (ratio of diffusion to drift) governs qualitative properties of the sample paths, including degree of randomization and intermittency, and applies the method to daily versus intraday upstream migration counts of Ayu (Plecoglossus altivelis altivelis), concluding that the daily regime exhibits a distinctive Feller index indicating qualitatively less randomization and intermittency than the intraday regime.

Significance. If the central distinction survives robustness checks, the work supplies a mathematically grounded method for comparing collective motion across timescales via the Feller index of diffusion bridges. The explicit guarantee of unique existence once coefficients are fixed is a clear technical strength that could be leveraged in other ecological time-series settings.

major comments (2)
  1. [Application study on Ayu migration] Application study: the claim that daily and intraday data correspond to distinctive Feller indices (and therefore qualitatively different intermittency) rests on post-fit drift and diffusion coefficients without reported uncertainty quantification, error bars on the fitted curves, or sensitivity tests to alternative parameterizations of the average and variance functions. Because the Feller index is computed directly from these curves, any instability in the fitting step directly affects the load-bearing distinction.
  2. [Diffusion bridge construction] Diffusion-bridge section: the manuscript states that unique existence is guaranteed once coefficients are fixed, yet does not verify that the standard Feller-condition link to boundary behavior and path intermittency continues to hold for the time-inhomogeneous bridges with pinned endpoints used here; explicit simulation or analytic confirmation of this link is required for the qualitative interpretation.
minor comments (2)
  1. The specific functional forms chosen for the time-dependent average and variance curves should be stated explicitly, together with the optimization procedure used to fit them to the count data.
  2. [Mathematical framework] Cross-reference the precise theorem or proposition that establishes unique existence of the bridges once the coefficients are fixed.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments that highlight important aspects of robustness and verification. We address each major comment below and describe the revisions we will incorporate.

read point-by-point responses

  1. Referee: [Application study on Ayu migration] Application study: the claim that daily and intraday data correspond to distinctive Feller indices (and therefore qualitatively different intermittency) rests on post-fit drift and diffusion coefficients without reported uncertainty quantification, error bars on the fitted curves, or sensitivity tests to alternative parameterizations of the average and variance functions. Because the Feller index is computed directly from these curves, any instability in the fitting step directly affects the load-bearing distinction.

    Authors: We agree that uncertainty quantification is essential to support the distinction in Feller indices. In the revised manuscript we will add bootstrap-based standard errors and 95% confidence bands on the fitted average and variance curves for both the daily and intraday regimes. We will also perform sensitivity analyses by refitting with alternative parameterizations (higher-degree polynomials and cubic splines with varied knot placements) and report the resulting range of Feller indices, confirming that the qualitative ordering (daily less intermittent than intraday) is preserved across these choices. revision: yes

  2. Referee: [Diffusion bridge construction] Diffusion-bridge section: the manuscript states that unique existence is guaranteed once coefficients are fixed, yet does not verify that the standard Feller-condition link to boundary behavior and path intermittency continues to hold for the time-inhomogeneous bridges with pinned endpoints used here; explicit simulation or analytic confirmation of this link is required for the qualitative interpretation.

    Authors: We acknowledge that the link between the Feller index and path intermittency, while standard for time-homogeneous diffusions, requires explicit confirmation in the time-inhomogeneous pinned-bridge setting. In the revision we will add a dedicated subsection containing Monte Carlo simulations of sample paths generated from the fitted time-inhomogeneous bridges. These simulations will demonstrate that the daily regime (higher Feller index) produces visibly smoother, less intermittent trajectories than the intraday regime, thereby validating the qualitative interpretation for our specific bridges. revision: yes

Circularity Check

1 steps flagged

Feller indices and intermittency claims reduce directly to fitted mean/variance curves on the same data

specific steps
  1. fitted input called prediction [Abstract]
    "Drift and diffusion coefficients of these bridges are determined based on time-dependent parameterized average and variance curves fitted against fish count data, with which the unique existence of their solutions is rigorously guaranteed. We show that sample paths of the diffusion bridges have qualitatively distinctive properties depending on the Feller condition, namely, the ratio between the sizes of diffusion and drift. ... Particularly, we discuss that the daily and intraday fish count data correspond to distinctive Feller indices, showing that the former is qualitatively less randomized."

    Feller index is the ratio of diffusion to drift coefficients; both coefficients are set directly from the fitted average and variance curves to the fish count data. The reported distinction between daily and intraday regimes (and the associated claim of different randomization/intermittency) is therefore the immediate numerical outcome of the chosen parameterization and fit, not a separate prediction.

full rationale

The derivation fits time-dependent parameterized average and variance curves to fish count data, defines drift and diffusion coefficients from those curves, computes the Feller ratio (diffusion/drift) from the same coefficients, and then states that the data exhibit distinctive indices and qualitative intermittency properties. This chain makes the central distinction a direct output of the fitting parameterization rather than an independent prediction or derivation from first principles. The SDE existence guarantee is external, but the load-bearing interpretation of Feller condition as distinguishing daily vs intraday regimes is not.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The model rests on standard SDE existence theorems once coefficients are given, plus the assumption that fitted curves represent true drift and diffusion. No new entities are postulated.

free parameters (1)
  • time-dependent parameterized average and variance curves
    Fitted directly to fish count data to define drift and diffusion coefficients of the bridges.
axioms (1)
  • standard math Unique existence of solutions to the nonlinear SDE with pinned boundary conditions once drift and diffusion are fixed
    Invoked to guarantee well-posedness of the diffusion bridges.

pith-pipeline@v0.9.0 · 5498 in / 1245 out tokens · 34189 ms · 2026-05-16T06:50:00.457593+00:00 · methodology

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Reference graph

Works this paper leans on

71 extracted references · 71 canonical work pages

  1. [1]

    Deutsch, A., Friedl, P., Preziosi, L., & Theraulaz, G. (2020). Multi -scale analysis and modelling of collective migration in biological systems. Philosophical Transactions of the Royal Society B, 375(1807), 20190377. https://doi.org/10.1098/rstb.2019.0377

    work page doi:10.1098/rstb.2019.0377 2020

  2. [2]

    J., Dalwadi, M

    Ridgway, W. J., Dalwadi, M. P., Pearce, P., & Chapman, S. J. (2023). Motility -induced phase separation mediated by bacterial quorum sensing. Physical review letters, 131(22), 228302. https://doi.org/10.1103/PhysRevLett.131.228302

    work page doi:10.1103/physrevlett.131.228302 2023

  3. [3]

    (2025-1)

    Smith, A., Ghosh, D., Tan, A., Cheng, X., & Daoutidis, P. (2025-1). Multi-scale causality in active matter. Computers & Chemical Engineering, 197, 109052. https://doi.org/10.1016/j.compchemeng.2025.109052

    work page doi:10.1016/j.compchemeng.2025.109052 2025

  4. [4]

    K., & Haest, B

    Bauer, S., Tielens, E. K., & Haest, B. (2024). Monitoring aerial insect biodiversity: a radar perspective. Philosophical Transactions of the Royal Society B, 379(1904), 20230113. https://doi.org/10.1186/s40462-024-00496-4

    work page doi:10.1186/s40462-024-00496-4 2024

  5. [5]

    K., Sekhon, G

    Kumar, S., Kler, T. K., Sekhon, G. S., & Sahni, T. (2024). Impacts on avian migratory patterns due to climate change and hormonal disruption: a review. Mitigation and Adaptation Strategies for Global Change , 29(7), 69. https://doi.org/10.1007/s11027-024- 10163-z

    work page doi:10.1007/s11027-024- 2024

  6. [6]

    B., Piland, N

    Victoria-Lacy, L., Couto, T. B., Piland, N. C., Dámaso, J., Fernandes, S., Athayde, S., & Anderson, E. P. (2025). Amazonian fish migration as a social-cultural-ecological process. People and Nature, 7(12), 3297 -3312. https://doi.org/10.1002/pan3.70190

    work page doi:10.1002/pan3.70190 2025

  7. [7]

    M., Carturan, B

    Atkinson, E. M., Carturan, B. S., Atkinson, C. P., Bateman, A. W., Connors, K., Hertz, E., & Peacock, S. J. (2025). Monitorin g for fisheries or for fish? Declines in monitoring of salmon spawners continue despite a conservation crisis. Canadian Journal of Fisheries and Aquatic Sciences, 82, 1-18. https://doi.org/10.1139/cjfas-2024-0387

    work page doi:10.1139/cjfas-2024-0387 2025

  8. [8]

    Chen, D., Li, S., & Wang, K. (2012). Enhancement and conservation of inland fisheries resources in China. Environmental Biology of Fishes, 93(4), 531 -545. https://doi.org/10.1007/s10641-011-9948-2

    work page doi:10.1007/s10641-011-9948-2 2012

  9. [9]

    Sunoko, R., & Huang, H. W. (2014). Indonesia tuna fisheries development and future strategy. Marine Policy, 43, 174 -183. https://doi.org/10.1016/j.marpol.2013.05.011

    work page doi:10.1016/j.marpol.2013.05.011 2014

  10. [10]

    D., Plumb, J

    Smith, C. D., Plumb, J. M., Adams, N. S., & Wyatt, G. J. (2021). Predator and prey events at the entrance of a surface -oriented fish collector at North Fork Dam, Oregon. Fisheries Management and Ecology, 28(2), 172-182. https://doi.org/10.1111/fme.12465

    work page doi:10.1111/fme.12465 2021

  11. [11]

    flowing spaces

    Zumbrägel, C. (2025). Eel on the move: fish migration and the construction of “flowing spaces” on the Rhine and Weser Rivers (1880–1930). Water History, 17(1), 77-101. https://doi.org/10.1007/s12685-024-00340-x

    work page doi:10.1007/s12685-024-00340-x 2025

  12. [12]

    Seyedhashemi, H., Drouineau , H., Arevalo, E., Legrand, M., Moatar, F., & Maire, A. (2025). Climate -induced changes in river hydrological and thermal conditions in a large basin: implications for diadromous fish migration. Canadian Journal of Fisheri es and Aquatic Sciences, 82, 1-12. https://doi.org/10.1139/cjfas-2024-0208

    work page doi:10.1139/cjfas-2024-0208 2025

  13. [13]

    G., Williams, C

    Warnock, W. G., Williams, C. H., & Teather, M. J. (2025). Spring climate warming is associated with earlier spawn timing of a n adfluvial trout population. Canadian Journal of Fisheries and Aquatic Sciences, 82, 1-11. https://doi.org/10.1139/cjfas-2025-0036

    work page doi:10.1139/cjfas-2025-0036 2025

  14. [14]

    F., Bennett, G., Beaumont, W

    Artero, C., Strøm, J. F., Bennett, G., Beaumont, W. A., Lecointre, T., Cirot, A., ... & Lauridsen, R. (2025). Diversity of sea trout marine migration routes in the English Channel. Animal Biotelemetry, 13(1), 18. https://doi.org/10.1186/s40317 -025-00413-5

    work page doi:10.1186/s40317 2025

  15. [15]

    D., Fanson, B

    Thiem, J. D., Fanson, B. G., Ryan, D., Butler, G. L., Crook, D. A., Harding, D. J., ... & Stuart, I. (2025). Repeated barrier drown- out is required to facilitate long-distance migration of a potamodromous fish. Aquatic Sciences, 87(4), 104. https://doi.org/10.1007/s00027-025-01228-5

    work page doi:10.1007/s00027-025-01228-5 2025

  16. [16]

    Q., Carey, C

    Paíz, R., Thomas, R. Q., Carey, C. C., de Eyto, E., Jones, I. D., Delany, A. D., ... & Jennings, E. (2025). Near -term lake water temperature forecasts can be used to anticipate the ecological dynamics of freshwater species. Ecosphere, 16(7), e70335. https://doi.org/10.1002/ecs2.70335

    work page doi:10.1002/ecs2.70335 2025

  17. [17]

    Wang, L., & Huang, Z. (2024). Passive drifting and high mortality rate of released subadult Chinese sturgeons in the Yangtze River. Reviews in Fish Biology and Fisheries, 34(1), 201 -219. https://doi.org/10.1007/s11160-023-09804-4

    work page doi:10.1007/s11160-023-09804-4 2024

  18. [18]

    P., & Emeliyanenko, P

    Lobyrev, F., Gallagher, C. P., & Emeliyanenko, P. (2023). A mathematical model predicting the abundance and spatio -temporal dispersal of adfluvial salmonid (Salvel inus malma) fry in a stream. Ecological Informatics , 78, 102359. https://doi.org/10.1016/j.ecoinf.2023.102359

    work page doi:10.1016/j.ecoinf.2023.102359 2023

  19. [19]

    Padoan, F., Calvani, G., De Cesare, G., & Perona, P. (2025). Hydraulic drive framework on habitat suitability enhances movement bias of brown trout in stream networks. Scientific Reports, 15(1), 16688. https://doi.org/10.1038/s41598-025-00216-x

    work page doi:10.1038/s41598-025-00216-x 2025

  20. [20]

    Alrabeei, S., Rahman, T., & Subbey, S. (2025). A machine learning framework for modeling Barents Sea Capelin spawning migration. Reviews in Fish Biology and Fisheries, 1 -19. https://doi.org/10.1007/s11160-025-09997-w

    work page doi:10.1007/s11160-025-09997-w 2025

  21. [21]

    (2025-2) Superposition of interacting stochastic processes with memory and its application to migrating fish counts

    Yoshioka, H. (2025-2) Superposition of interacting stochastic processes with memory and its application to migrating fish counts. Chaos, Solitons & Fractals, 192, 115911. https://doi.org/10.1016/j.chaos.2024.115911

    work page doi:10.1016/j.chaos.2024.115911 2025

  22. [22]

    Ladoux, P., Legrand, M., Portafaix, P., Buisson, L., & Laffaille, P. (2025). Synchrony between reproductive patterns and photoperiod in Allis shad (Alosa alosa L.) in the Loire River catchment. Aquatic Ecology, 59(4), 1183 -1198. https://doi.org/10.1007/s10452-025-10219-5

    work page doi:10.1007/s10452-025-10219-5 2025

  23. [23]

    E., Beaumont, W

    Artero, C., Marsh, J. E., Beaumont, W. A., Lecointre, T., & Lauridsen, R. B. (2025). Spatial –temporal variation in the vertical behaviour of sea trout kelts during their marine phase. Reviews in Fish Biology and Fisheries, 1 -21. https://doi.org/10.1007/s11160-025-09963-6

    work page doi:10.1007/s11160-025-09963-6 2025

  24. [24]

    P., Sonny, D., Colson, D., Dierckx, A., & Ovidio, M

    Benitez, J. P., Sonny, D., Colson, D., Dierckx, A., & Ovidio, M. (2025). Hydroelectric power plant and upstream fish migratio n: evaluation of the efficiency of a behavioural barrier. Journal of Ecohydraulics, 1 -14. https://doi.org/10.1080/24705357.2025.2533868

    work page doi:10.1080/24705357.2025.2533868 2025

  25. [25]

    N., & Benitez, J

    Ovidio, M., Renardy, S., Dierckx, A., Matondo, B. N., & Benitez, J. P. (2021). Improving bypass performance and passage success of Atlantic salmon smolts at an old fish -hostile hydroelectric power station: A challenging task. Ecological Engineering, 160, 106148. https://doi.org/10.1016/j.ecoleng.2021.106148

    work page doi:10.1016/j.ecoleng.2021.106148 2021

  26. [26]

    & Bai, Y

    Chen, X., Shi, X., Deng, X., Rasta, M., Tan, J., Wang, Y., ... & Bai, Y. (2025). A multiple -behaviors virtual fish model for simulating fish trajectory in vertical slot fishways. Journal of Fish Biology. Online published. https://doi.org/10.1111/jfb.16064

    work page doi:10.1111/jfb.16064 2025

  27. [27]

    R., Zielinski, D

    Kerr, J. R., Zielinski, D. P., Goodwin, R. A., Holbrook, C. M., & McLaughlin, R. L. (2025). Upriver migrating sea lamprey exhibit similar responses to hydrodynamic features as other up and downriver -moving species. Frontiers in Freshwater Science, 3, 1528481. https://doi.org/10.3389/ffwsc.2025.1528481

    work page doi:10.3389/ffwsc.2025.1528481 2025

  28. [28]

    & Yao, W

    Liu, S., Wang, N., Gualtieri, C., Zhang, C., Cao, C., Chen, J., ... & Yao, W. (2025). Fish migration modeling and habitat assessment in a complex fluvial system. Journal of Environmental Management, 374, 124146. https://doi.org/10.1016/j.jenvman.2025.124146 25

    work page doi:10.1016/j.jenvman.2025.124146 2025

  29. [29]

    Yoshioka, H. (2025). CIR bridge for modeling of fish migration on sub-hourly scale. Chaos, Solitons & Fractals, 199, Part 3, 116874. https://doi.org/10.1016/j.chaos.2025.116874

    work page doi:10.1016/j.chaos.2025.116874 2025

  30. [30]

    What Is the Turbulence Problem, and When May We Regard It as Solved?

    Sreenivasan, K. R., & Schumacher, J. (2025). What is the turbulence problem, and when may we regard it as solved?. Annual Review of Condensed Matter Physics, 16(1), 121 -143. https://doi.org/10.1146/annurev-conmatphys-031620-095842

    work page doi:10.1146/annurev-conmatphys-031620-095842 2025

  31. [31]

    D., Aikens, E

    Bontekoe, I. D., Aikens, E. O., Schlicksupp, A., Blumenstiel, L., Honorato, R. G., Jorzik, I., & Flack, A. (2025). The study of social animal migrations: a synthesis of the past and guidelines for future research. Proceedings B, 292(2049), 20242726. https://doi.org/10.1098/rspb.2024.2726

    work page doi:10.1098/rspb.2024.2726 2025

  32. [32]

    C., & Laskowski, K

    Ioannou, C. C., & Laskowski, K. L. (2023). A multi -scale review of the dynamics of collective behaviour: from rapid responses to ontogeny and evolution. Philosophical transactions of the royal society B, 378(1874), 20220059. https://doi.org/10.1098/rstb.2022.0059

    work page doi:10.1098/rstb.2022.0059 2023

  33. [33]

    H., Davidson, J

    Sridhar, V. H., Davidson, J. D., Twomey, C. R., Sosna, M. M., Nagy, M., & Couzin, I. D. (2023). Inferring social influence in animal groups across multiple timescales. Philosophical Transactions of the Royal Society B, 378(1874), 20220062. https://doi.org/10.1098/rstb.2022.0062

    work page doi:10.1098/rstb.2022.0062 2023

  34. [34]

    Mao, X. (2007). Stochastic differential equations and applications. Elsevier

    work page 2007

  35. [35]

    C., Ingersoll, J

    Cox, J. C., Ingersoll, J. E., & Ross, S. A. (1985). A theory of the term structure of interest rates. Econometrica, 53(2), 38 5-407. https://doi.org/10.1142/5860

    work page doi:10.1142/5860 1985

  36. [36]

    Alfonsi, A. (2015). Affine diffusions and related processes: Simulation, theory and applications. Springer, Cham

    work page 2015

  37. [37]

    Kohatsu-Higa, A., & Tamura, Y. (2025). Representation and Integration by Parts Formulas for Affine Processes. Asia -Pacific Financial Markets, 1-15. https://doi.org/10.1007/s10690 -025-09574-y

    work page doi:10.1007/s10690 2025

  38. [38]

    Mittal, P., & Selvamuthu, D. (2025). Options pricing with Markov regime switching Heston volatility Hull –White interest rates and stochastic intensity. Probability in the Engineering and Informational Sciences, 39(2), 243 -259. https://doi.org/10.1017/S0269964824000202

    work page doi:10.1017/s0269964824000202 2025

  39. [39]

    Atance, D., & Navarro, E. (2024). Revisiting key mortality rate models: novel findings and application of CIR processes to describe mortality trends. Decisions in Economics and Finance, 1 -38. Online published. https://doi.org/10.1007/s10203 -024- 00481-x

    work page doi:10.1007/s10203 2024

  40. [40]

    Sarkar, S., Murali, K., Chandra, A., Das, S., & Varma, H. M. (2025). Spatio -temporal Simulation of Laser Speckles using Stochastic Differential Equations. IEEE Journal of Selected Topics in Quantum Electronics. Online published. https://doi.org/10.1109/JSTQE.2025.3571385

    work page doi:10.1109/jstqe.2025.3571385 2025

  41. [41]

    Abonongo, J., & Chidzalo, P. (2024). Synthesis Weibull Stochastic Differential Equation: Properties and application. Scientif ic African, 23, e02074. https://doi.org/10.1016/j.sciaf.2024.e02074

    work page doi:10.1016/j.sciaf.2024.e02074 2024

  42. [42]

    Chidzalo, P., Beyamu, D., Mutepuwa, J., Kambale, C., Dzupire, N., Kaombe, P., & Chidothi, P. (2025). Modeling the impact of tropical cyclone intensity on rainfall under stochastic processes. Modeling Earth Systems and Environment, 11(5), 365. https://doi.org/10.1007/s40808-025-02563-0

    work page doi:10.1007/s40808-025-02563-0 2025

  43. [43]

    De Col, A., Gnoatto, A., & Grasselli, M. (2013). Smiles all around: FX joint calibration in a multi -Heston model. Journal of Banking & Finance, 37(10), 3799 -3818. https://doi.org/10.1016/j.jbankfin.2013.05.031

    work page doi:10.1016/j.jbankfin.2013.05.031 2013

  44. [44]

    Okhrin, O., Rockinger, M., & Schmid, M. (2025). Observations concerning the estimation of Heston’s stochastic volatility model using HF data. Statistical Papers, 66(4), 90. https://doi.org/10.1007/s00362 -025-01710-0

    work page doi:10.1007/s00362 2025

  45. [45]

    Abdellatif, M., Friesen, M., Kuchling, P., & Rüdiger, B. (2025). A large deviations principle for time averages of continuous-state branching processes with immigration. Stochastics, 97(4), 520 -538. https://doi.org/10.1080/17442508.2025.2493815

    work page doi:10.1080/17442508.2025.2493815 2025

  46. [46]

    Abi Jaber, E., & Gérard, L. A. (2025). Signature volatility models: pricing and hedging with Fourier. SIAM Journal on Financi al Mathematics, 16(2), 606-642. https://doi.org/10.1137/24M1636952

    work page doi:10.1137/24m1636952 2025

  47. [47]

    Le Floc’h, F. (2021). Pricing American options with the Runge –Kutta–Legendre finite difference scheme. International Journal of Theoretical and Applied Finance, 24(03), 2150018. https://doi.org/10.1142/S0219024921500187

    work page doi:10.1142/s0219024921500187 2021

  48. [48]

    Hefter, M., & Herzwurm, A. (2018). Strong convergence rates for Cox –Ingersoll–Ross processes—full parameter range. Journal of Mathematical Analysis and Applications, 459(2), 1079 -1101. https://doi.org/10.1016/j.jmaa.2017.10.076

    work page doi:10.1016/j.jmaa.2017.10.076 2018

  49. [49]

    (2025 -3) A minimization principle behind the diffusion bridge of diurnal fish migration

    Yoshioka, H. (2025 -3) A minimization principle behind the diffusion bridge of diurnal fish migration. Preprint. https://arxiv.org/abs/2509.03824

    work page arXiv 2025

  50. [50]

    E., Buijse, A

    Edwards, J. E., Buijse, A. D., Winter, H. V., & Bijleveld, A. I. (2025). Seasonal coastal residency and large-scale migration of two grey mullet species in temperate European waters. Movement Ecology, 13(1), 2. https://doi.org/10.1186/s40462 -024-00528-z

    work page doi:10.1186/s40462 2025

  51. [51]

    M., Pierce, S

    Kastl, B., Obedzinski, M., Carlson, S. M., Pierce, S. N., van Docto, M. M., Skorko, K. W., ... & Grantham, T. E. (2025). Navigating Shallow Streams: Effects of Changing Stream Water Depths on Outmigration of Endangered Coho Salmon. River Research and Applications. Online published. https://doi.org/10.1002/rra.4466

    work page doi:10.1002/rra.4466 2025

  52. [52]

    & Swanson, H

    Smith, R., Hitkolok , E., Dumond, A., DePasquale, S., Thibault, H., Weinstein, S., ... & Swanson, H. (2025 -2). Environment influences migration timing of cold-adapted salmonids (Salvelinus alpinus and S. malma malma) in the Canadian Arctic. Canadian Journal of Fisheries and Aquatic Sciences, 82, 1 -20. https://doi.org/10.1139/cjfas-2024-0385

    work page doi:10.1139/cjfas-2024-0385 2025

  53. [53]

    I., Britton, J

    Yeldham, M. I., Britton, J. R., Crundwell, C., Davies, P., Dodd, J. R., Grzesiok, C., ... & Bolland, J. D. (2025). Contrastin g responses to riverine barrier modification and fish pass provision in two anadromous non-salmonid species during their spawning migrations. Journal of Applied Ecology. Online published. https://doi.org/10.1111/1365-2664.70093

    work page doi:10.1111/1365-2664.70093 2025

  54. [54]

    Yoshioka, H., & Yamazaki, K. (2025). a jump-driven self-exciting stochastic fish migration model and its fisheries applications. Natural Resource Modeling, 38(1), e12419. https://doi.org/10.1111/nrm.12419

    work page doi:10.1111/nrm.12419 2025

  55. [55]

    (2025-4)

    Yoshioka, H. (2025-4). Non-negative diffusion bridge of the McKean -Vlasov type: analysis of singular diffusion and application to fish migration. Preprint. https://arxiv.org/abs/2510.03692

    work page arXiv 2025

  56. [56]

    Hirono, Y., Tanaka, A., & Fukushima, K. (2024). Hirono, Y., Tanaka, A., & Fukushima, K. (2024, July). Understanding Diffusion Models by Feynman’s Path Integral. In International Conference on Machine Learning (pp. 18324 -18351). PMLR. https://proceedings.mlr.press/v235/hirono24a.html

    work page 2024

  57. [57]

    Karatzas, I., & Shreve, S. (2014). Brownian motion and stochastic calculus. Springer, New York

    work page 2014

  58. [58]

    & Laffaille, P

    Legrand, M., Briand, C., Buisson, L., Besse, T., Artur, G., Azam, D., ... & Laffaille, P. (2021). Diadromous fish modified ti ming of upstream migration over the last 30 years in France. Freshwater Biology, 66(2), 286 -302. https://doi.org/10.1111/fwb.13638

    work page doi:10.1111/fwb.13638 2021

  59. [59]

    T., Cubbage, M

    Koenigbauer, S. T., Cubbage, M. L., Warren, L. D., Tellier, J. M., Selz, O. M., Sass, G. G., & Höök, T. O. (2025). Fish reproductive phenology shifts with increasing temperature and year. Biology Letters, 21(1), 20240240. https://doi.org/10.1098/rsbl.2024.0240 26

    work page doi:10.1098/rsbl.2024.0240 2025

  60. [60]

    Y., & Chen, Y

    Chang, H. Y., & Chen, Y. (2024). Shifting spawning phenology in Hudson River American Shad. Marine and Coastal Fisheries, 16(5), 10312. https://doi.org/10.1002/mcf2.10312

    work page doi:10.1002/mcf2.10312 2024

  61. [61]

    Nagayama, S., Fujii, R., Harada, M., & Sueyoshi, M. (2023). Low water temperature and increased discharge trigger downstream spawning migration of ayu Plecoglossus altivelis. Fisheries Science, 89(4), 463 -475. https://doi.org/10.1007/s12562 -023-01694- 6

    work page doi:10.1007/s12562 2023

  62. [62]

    Erraoui, M., Hilbert, A., & Louriki, M. (2020). Bridges with random length: Gamma case. Journal of Theoretical Probability, 33(2), 931-953. https://doi.org/10.1007/s10959-019-00955-4

    work page doi:10.1007/s10959-019-00955-4 2020

  63. [63]

    Louriki, M. (2022). Brownian bridge with random length and pinning point for modelling of financial information. Stochastics, 94(7), 973-1002. https://doi.org/10.1080/17442508.2021.2017438

    work page doi:10.1080/17442508.2021.2017438 2022

  64. [64]

    Watanabe, S. (2022). Migration of Fishes in Japan. In Fish Diversity of Japan: Evolution, Zoogeography, and Conservation (pp. 221-236). Singapore: Springer Nature Singapore. https://doi.org/10.1007/978-981-16-7427-3_13

    work page doi:10.1007/978-981-16-7427-3_13 2022

  65. [65]

    D., Cogan, J., Durban, J

    Stewart, J. D., Cogan, J., Durban, J. W., Fearnbach, H., Ellifrit, D. K., Malleson, M., Pinnow, M., & Balcomb, K. C. (2023). Traditional summer habitat use by Southern Resident killer whales in the Salish Sea is linked to Fraser River Chinook salmon . Marine Mammal Science, 39(3), 858-875. https://doi.org/10.1111/mms.13012

    work page doi:10.1111/mms.13012 2023

  66. [66]

    J., & Hawkshaw, M

    Xie, Y., Walters, C. J., & Hawkshaw, M. A. (2025). A species-specific catchability model to partition hydroacoustic total salmon counts Open Access. North American Journal of Fisheries Management, 45 (1), 61-75. https://doi.org/10.1093/najfmt/vqaf010

    work page doi:10.1093/najfmt/vqaf010 2025

  67. [67]

    M., Sigourney, D

    Weaver, D. M., Sigourney, D. B., Delucia, M. B., & Zydlewski, J. D. (2021). Characterizing Downstream Migration Timing of American Eels Using Commercial Catch Data in the Penobscot and Delaware Rivers . Marine and Coastal Fisheries: Dynamics, Management, and Ecosystem Science, 13, 534 -547. https://doi.org/10.1002/mcf2.10182

    work page doi:10.1002/mcf2.10182 2021

  68. [68]

    Abi Jaber, E. (2024). Simulation of square -root processes made simple: applications to the Heston model. Preprint. https://arxiv.org/abs/2412.11264

    work page arXiv 2024

  69. [69]

    Z., Reis-Santos, P., Gonzalez, J

    Ng, C. Z., Reis-Santos, P., Gonzalez, J. G., Gillanders, B. M., Saleh, M. F., & Ong, J. J. (2025). A non-linear statistical framework to investigate changes in life history patterns within and among fish populations. Reviews in Fish Biology and Fisheries, Published online. https://doi.org/10.1007/s11160-025-09993-0

    work page doi:10.1007/s11160-025-09993-0 2025

  70. [70]

    Privault, N. (2025). Chapter 4: Brownian Motion and Stochastic Calculus, Notes on Stochastic Finance . Available at https://personal.ntu.edu.sg/nprivault/MA5182/brownian -motion-stochastic-calculus.pdf, last accessed on December 19, 2025

    work page 2025

  71. [71]

    Jacod, J., & Protter, P. (2004). Random Variables. In: Probability Essentials. Springer, Berlin, Heidelberg

    work page 2004