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pith:25ZR7DUN

pith:2026:25ZR7DUNBEHO47C2Z2PZZ32YZR

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Splitting schemes and estimators for stochastic differential equations with H\"older multiplicative noise

Bowen Fang, Dario Span\`o, Massimiliano Tamborrino

Splitting schemes based on the Lamperti transform produce strongly convergent and state-space-preserving pseudo-likelihood estimators for SDEs with Hölder multiplicative noise.

arxiv:2605.16900 v1 · 2026-05-16 · stat.ME · math.ST · stat.TH

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Claims

C1strongest claim

We introduce the first explicit pseudo-likelihood estimators based on numerical splitting schemes that are both strong mean-square convergent and state space preserving for this class of SDEs. We prove strong mean-square convergence, state space preservation, and improved robustness with respect to the discretisation step compared to Euler-Maruyama-based methods. We further establish consistency and asymptotic normality of the LT estimator.

C2weakest assumption

The SDE admits a reducible decomposition via the Lamperti transform that allows explicit splitting into drift and diffusion components while preserving the Hölder regularity and local Lipschitz conditions needed for the convergence and likelihood derivations (abstract and introduction).

C3one line summary

New splitting-scheme-based pseudo-likelihood estimators for SDEs with Hölder multiplicative noise that achieve strong convergence, state-space preservation, consistency, and asymptotic normality.

References

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[1] D.-H. Ahn and B. Gao. A Parametric Nonlinear Model of Term Structure Dynamics. Rev. Financ. Stud., 12(4):721–762, 1999. ISSN 0893-9454. URLhttps://www.jstor.org/ stable/2645963 1999

[2] Y. Ait-Sahalia. Maximum Likelihood Estimation of Discretely Sampled Diffusions: A Closed-form Approximation Approach. Econometrica, 70(1):223–262, 2002. ISSN 0012- 9682, 1468-0262. doi: 10.1111/1468-0 2002 · doi:10.1111/1468-0262.00274

[3] N. Berglund and D. Landon. Mixed-mode oscillations and interspike interval statistics in the stochastic fitzhugh-nagumo model. Nonlinearity, 25:2303–2335, 2012 2012

[4] A. Beskos, O. Papaspiliopoulos, G. O. Roberts, and P. Fearnhead. Exact and computation- ally efficient likelihood-based estimation for discretely observed diffusion processes (with discussion). J. Roy 2006

[5] B. M. Bibby and M. Sørensen. Martingale Estimation Functions for Discretely Observed Diffusion Processes. Bernoulli, 1(1/2):17–39, 1995. ISSN 1350-7265. doi: 10.2307/3318679. URLhttps://www.jstor.org/ 1995 · doi:10.2307/3318679

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Receipt and verification

First computed	2026-05-20T00:03:29.105429Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d7731f8e8d090eee7c5ace9f9cef58cc737b7f18af6e25b253c8a71d740e8b0a

Aliases

arxiv: 2605.16900 · arxiv_version: 2605.16900v1 · doi: 10.48550/arxiv.2605.16900 · pith_short_12: 25ZR7DUNBEHO · pith_short_16: 25ZR7DUNBEHO47C2 · pith_short_8: 25ZR7DUN

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curl -sH 'Accept: application/ld+json' https://pith.science/pith/25ZR7DUNBEHO47C2Z2PZZ32YZR \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: d7731f8e8d090eee7c5ace9f9cef58cc737b7f18af6e25b253c8a71d740e8b0a

Canonical record JSON

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    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "stat.ME",
    "submitted_at": "2026-05-16T09:22:43Z",
    "title_canon_sha256": "75f7b3e9ec7cc00930b0e0d8cd11cd3d278caab021f6c2035935236f47dbc803"
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