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Paper Citation Record · LEDGER

Deep Learning Method for Stationary Distribution of Reflected Brownian Motion

As of 9 August 2026, this Paper Citation Record lists 23 of 23 outbound references and 0 inbound Pith citation observations for arXiv:2607.08091.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2607.08091 v1

Coverage vector

measured 23 of 23 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-07-10T13:13:57.925643Z

measured 23 of 23 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-09T06:31:02.800959+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: cited_works

Reference resolution

23 of 23 outbound references displayed

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  • verified fuzzy19
  • unresolved2
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation df602404-a8fa-4b02-8411-d18ab2f77343 · outbound

This paper cites A multi-dimensional srbm: geometric views of its product form stationary distribution.Queueing Systems, 78(4):313–335, 2014.

Deep Learning Method for Stationary Distribution of Reflected Brownian Motion A multi-dimensional srbm: geometric views of its product form stationary distribution.Queueing Systems, 78(4):313–335, 2014

Reference 1

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

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Observation a7b84cb8-a6c6-45d8-bcef-0ce906339526 · outbound

This paper cites Efficient steady-state simulation of high-dimensional stochastic networks.Stochastic Systems, 11(2):174–192, 2021.

Deep Learning Method for Stationary Distribution of Reflected Brownian Motion Efficient steady-state simulation of high-dimensional stochastic networks.Stochastic Systems, 11(2):174–192, 2021

Reference 2

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

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Observation 5f845631-d6a9-45df-a0f6-5f8e13718071 · outbound

This paper cites A unified framework for numerically inverting laplace trans- forms.INFORMS Journal on Computing, 18(4):408–421, 2006.

Deep Learning Method for Stationary Distribution of Reflected Brownian Motion A unified framework for numerically inverting laplace trans- forms.INFORMS Journal on Computing, 18(4):408–421, 2006

Reference 3

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

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Observation 2321a8dc-4d40-48a8-bdb6-883f6f6e6eb3 · outbound

This paper cites Deep learning for computing convergence rates of markov chains.Advances in Neural Information Processing Systems, 37:84777–84798, 2024.

Deep Learning Method for Stationary Distribution of Reflected Brownian Motion Deep learning for computing convergence rates of markov chains.Advances in Neural Information Processing Systems, 37:84777–84798, 2024

Reference 4

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raw_fallback, observed 2026-07-10T13:27:06.534089Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-07-10T13:13:57.925643Z digest=sha256:c581fe2be1325181ed1ec760446b8746985a11b08a4d05c90c3adb0358790943

Observation d78e5e5a-cf65-4e75-9253-87f69ecb8c94 · outbound

This paper cites Deep learning for markov chains: Lyapunov functions, poisson’s equation, and stationary distributions.Queueing Systems, 110(1):10, 2026.

Deep Learning Method for Stationary Distribution of Reflected Brownian Motion Deep learning for markov chains: Lyapunov functions, poisson’s equation, and stationary distributions.Queueing Systems, 110(1):10, 2026

Reference 5

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

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Observation 4d425897-e8b0-40e4-8c43-a40fa42b6eec · outbound

This paper cites an unresolved cited work.

Deep Learning Method for Stationary Distribution of Reflected Brownian Motion Unresolved cited work

Reference 6

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unresolved
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-07-10T13:13:57.925643Z digest=sha256:8cce29e3ab727713becacc676b0898e5564065f10fc300c45f14d715f9a95daf

Observation a120a5c8-98b9-4500-bd65-d625ca338b78 · outbound

This paper cites Solving high-dimensional partial differential equa- tions using deep learning.Proceedings of the National Academy of Sciences, 115(34):8505–8510, 2018.

Deep Learning Method for Stationary Distribution of Reflected Brownian Motion Solving high-dimensional partial differential equa- tions using deep learning.Proceedings of the National Academy of Sciences, 115(34):8505–8510, 2018

Reference 7

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verified fuzzy
raw_fallback, observed 2026-07-10T13:27:06.535802Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-07-10T13:13:57.925643Z digest=sha256:f14f56b2a6915cc1ed0419af8a4acc6d5dd706ded7a1982d43c6ddd266e42822

Observation 03e0789e-a543-4dbf-838c-e114a1bb2193 · outbound

This paper cites Dynamic control of stochastic matching systems in heavy traffic: An effective computational method for high-dimensional problems.arXiv preprint arXiv:2509.00809, 2025.

Deep Learning Method for Stationary Distribution of Reflected Brownian Motion Dynamic control of stochastic matching systems in heavy traffic: An effective computational method for high-dimensional problems.arXiv preprint arXiv:2509.00809, 2025

Reference 8

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arxiv_id, observed 2026-07-10T13:17:05.960303Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

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Observation 12cba751-e2e3-495a-8744-0bc4821e39e4 · outbound

This paper cites Dynamic scheduling of a multiclass queue in the halfin–whitt regime: A computational approach for high-dimensional problems.Management Science, 2025.

Deep Learning Method for Stationary Distribution of Reflected Brownian Motion Dynamic scheduling of a multiclass queue in the halfin–whitt regime: A computational approach for high-dimensional problems.Management Science, 2025

Reference 9

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raw_fallback, observed 2026-07-10T13:27:06.541160Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-07-10T13:13:57.925643Z digest=sha256:a4d982426ca748ef9934a87f9b5442b3b57ee237f0558700d75024a92d7185dd

Observation a8837ee7-dbba-4498-8411-430fc0b0d9ce · outbound

This paper cites A Computational Method for Solving the Stochastic Joint Replenishment Problem in High Dimensions.

Deep Learning Method for Stationary Distribution of Reflected Brownian Motion A Computational Method for Solving the Stochastic Joint Replenishment Problem in High Dimensions

Reference 10

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

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Observation fe1da968-bc6c-40fa-b8d1-460f04646437 · outbound

This paper cites Driftcontrolofhigh-dimensionalreflectedbrownian motion: Acomputationalmethodbasedonneuralnetworks.Stochastic Systems, 15(2):111–146, 2025.

Deep Learning Method for Stationary Distribution of Reflected Brownian Motion Driftcontrolofhigh-dimensionalreflectedbrownian motion: Acomputationalmethodbasedonneuralnetworks.Stochastic Systems, 15(2):111–146, 2025

Reference 11

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verified fuzzy
raw_fallback, observed 2026-07-10T13:27:06.521697Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-07-10T13:13:57.925643Z digest=sha256:43eb3c83207352ad07f04f0d2efe05169a30aac7c074e06cd46ee813f8b605cb

Observation c0829da0-d760-4b71-87ba-8c094d06c40f · outbound

This paper cites Singular control of (reflected) brownian motion: A computational method suitable for queueing applications.Queueing Systems, 108(3):215–251, 2024.

Deep Learning Method for Stationary Distribution of Reflected Brownian Motion Singular control of (reflected) brownian motion: A computational method suitable for queueing applications.Queueing Systems, 108(3):215–251, 2024

Reference 12

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verified fuzzy
raw_fallback, observed 2026-07-10T13:27:06.525241Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-07-10T13:13:57.925643Z digest=sha256:59d3f2c68a4777f7def8c6fbe8c12093e4c2f0d745f528a42efe935f9e98a479

Observation b272b427-e8ea-475a-a4dd-4394da1f8f01 · outbound

This paper cites Algorithms for solving high dimensional pdes: from nonlinear monte carlo to machine learning.Nonlinearity, 35(1):278, 2021.

Deep Learning Method for Stationary Distribution of Reflected Brownian Motion Algorithms for solving high dimensional pdes: from nonlinear monte carlo to machine learning.Nonlinearity, 35(1):278, 2021

Reference 13

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raw_fallback, observed 2026-07-10T13:27:06.517543Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-07-10T13:13:57.925643Z digest=sha256:8ac3ff4261a7b35a5ddc26d875b4d24ba1208c48cbcb1b2a20c9715fc7bdc368

Observation 4fec603d-f72b-460c-aba9-c82b00c33b1c · outbound

This paper cites Solving the quantum many-body problem with artificial neural networks.Science, 355(6325):602–606.

Deep Learning Method for Stationary Distribution of Reflected Brownian Motion Solving the quantum many-body problem with artificial neural networks.Science, 355(6325):602–606

Reference 14

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verified fuzzy
raw_fallback, observed 2026-07-10T13:27:06.515593Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-07-10T13:13:57.925643Z digest=sha256:333d6c3d53d835ffdb6a4193db5fb9593d1a6c0539cbe1c8372f7c9851ac3d9a

Observation de1a08ba-b1ed-402a-aef9-08e8605fa96a · outbound

This paper cites The deep ritz method: a deep learning-based numerical algorithm for solving variational problems.Communications in Mathematics and Statistics, 6(1):1–12.

Deep Learning Method for Stationary Distribution of Reflected Brownian Motion The deep ritz method: a deep learning-based numerical algorithm for solving variational problems.Communications in Mathematics and Statistics, 6(1):1–12

Reference 15

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raw_fallback, observed 2026-07-10T13:27:06.519804Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-07-10T13:13:57.925643Z digest=sha256:b5ba4d485a48c1b880c188343ea305cb118e5a76feb26e7555192800af5d8f0a

Observation e5a647e7-b511-45c6-a669-7b06c2b12a1f · outbound

This paper cites Dgm: A deep learning algorithm for solving partial differential equations.Journal of computational physics, 375:1339–1364.

Deep Learning Method for Stationary Distribution of Reflected Brownian Motion Dgm: A deep learning algorithm for solving partial differential equations.Journal of computational physics, 375:1339–1364

Reference 16

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-07-10T13:13:57.925643Z digest=sha256:d54c4178638fe882e87baf0bb01dd9b1e9113f019f4915ee88881bd8bdcb5fbc

Observation e0feccb6-895e-46d7-89e0-0be9be4f5b0e · outbound

This paper cites The accurate numerical inversion of laplace transforms.IMA Journal of Applied Mathematics, 23(1):97–120, 1979.

Deep Learning Method for Stationary Distribution of Reflected Brownian Motion The accurate numerical inversion of laplace transforms.IMA Journal of Applied Mathematics, 23(1):97–120, 1979

Reference 17

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raw_fallback, observed 2026-07-10T13:27:06.510325Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-07-10T13:13:57.925643Z digest=sha256:f282a2fdfd92145f668b4d3a2653aa2bb0d65c6f6ca7a9b8e887f19d51fb6bd4

Observation fdc06718-6455-4165-9398-092354141289 · outbound

This paper cites Optimizing talbot’s contours for the inversion of the laplace trans- form.SIAM Journal on Numerical Analysis, 44(6):2342–2362, 2006.

Deep Learning Method for Stationary Distribution of Reflected Brownian Motion Optimizing talbot’s contours for the inversion of the laplace trans- form.SIAM Journal on Numerical Analysis, 44(6):2342–2362, 2006

Reference 18

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raw_fallback, observed 2026-07-10T13:27:06.508687Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-07-10T13:13:57.925643Z digest=sha256:63aeb6f182482245c30b381d29ca47e5b32fb4d217060092e09d75bbae0bc913

Observation c1b4e0fb-07e1-4eea-8663-65c6e5a03ef9 · outbound

This paper cites Thefourier-seriesmethodforinvertingtransformsofprobability distributions.Queueing systems, 10(1):5–87, 1992.

Deep Learning Method for Stationary Distribution of Reflected Brownian Motion Thefourier-seriesmethodforinvertingtransformsofprobability distributions.Queueing systems, 10(1):5–87, 1992

Reference 19

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raw_fallback, observed 2026-07-10T13:27:06.512069Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-07-10T13:13:57.925643Z digest=sha256:b42ad279203717850ceb193005d0c5d2bba4ea9181dfa43ba0706dc332cd7656

Observation 56329684-a980-4db1-94e9-ed4dbcecb6ba · outbound

This paper cites Reflected brownian motion in an orthant: numerical methods for steady-state analysis.The Annals of Applied Probability, 2(1):65–86, 1992.

Deep Learning Method for Stationary Distribution of Reflected Brownian Motion Reflected brownian motion in an orthant: numerical methods for steady-state analysis.The Annals of Applied Probability, 2(1):65–86, 1992

Reference 20

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verified fuzzy
raw_fallback, observed 2026-07-10T13:27:06.505115Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-07-10T13:13:57.925643Z digest=sha256:f10910e404dacb4e9c1bb917842c3149ee863c2cc4ec26c063bf7277fd0f091b

Observation bc6e29e4-082f-4cf6-9ece-982cfbdeb32e · outbound

This paper cites The diffusion approximation for tandem queues in heavy traffic.Advances in Applied Probability, 10(4):886–905, 1978.

Deep Learning Method for Stationary Distribution of Reflected Brownian Motion The diffusion approximation for tandem queues in heavy traffic.Advances in Applied Probability, 10(4):886–905, 1978

Reference 21

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raw_fallback, observed 2026-07-10T13:27:06.506858Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-07-10T13:13:57.925643Z digest=sha256:1824812d4446a1dcdee47bd5f4e59668d6f9aecd30303a27e5c344708a857b1c

Observation 64ad0c39-29a0-4f92-8b7c-8f661a230c41 · outbound

This paper cites an unresolved cited work.

Deep Learning Method for Stationary Distribution of Reflected Brownian Motion Unresolved cited work

Reference 22

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unresolved
raw_fallback, observed 2026-07-10T13:27:06.513786Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-07-10T13:13:57.925643Z digest=sha256:e9708ead45c2ca7c49a39816b98132b027787ef710ee198ba2888a4e48443b4d

Observation f142982b-2a3a-40c7-bad2-247238955d74 · outbound

This paper cites Numerical computation of the moments of a probability distribution from its transform.Operations Research, 44(2):368–381, 1996.

Deep Learning Method for Stationary Distribution of Reflected Brownian Motion Numerical computation of the moments of a probability distribution from its transform.Operations Research, 44(2):368–381, 1996

Reference 23

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raw_fallback, observed 2026-07-10T13:27:06.526942Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-07-10T13:13:57.925643Z digest=sha256:1590d124c5ae77cecf35fc0b1c065ae163e66cc4d4f4d8892b70ad7fdb889c32

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