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pith:LZXGAG2K

pith:2026:LZXGAG2KFQ56FZYOG6Q23YQ26D

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Euler-Maruyama method for non-Wiener processes

Richard D.J.G. Ho

The Euler-Maruyama method generalizes to stochastic differential equations driven by a subset of Lévy processes rather than only Wiener processes.

arxiv:2605.16662 v1 · 2026-05-15 · cond-mat.stat-mech · nlin.AO

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Claims

C1strongest claim

The Euler-Maruyama method of discretising stochastic differential equations to non-Wiener processes is generalised. Non-Gaussian noise generated from a subset of Lévy processes can be used simply and often with more physical justification, for both additive and multiplicative noise. The results of the additive noise are shown to be equivalent to a derived master equation via the Kramers-Moyal expansion.

C2weakest assumption

That non-Gaussian fluctuations in the target systems originate from non-Wiener processes belonging to a usable subset of Lévy processes, and that the discretization preserves the necessary convergence and equivalence properties without additional restrictions on the noise.

C3one line summary

The Euler-Maruyama method is extended to non-Wiener Lévy processes for additive and multiplicative noise, yielding an example with superior physical results over geometric Brownian motion and equivalence to a master equation via Kramers-Moyal expansion.

References

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[1] M. B. Elowitz, A. J. Levine, E. D. Siggia, and P. S. Swain, Stochastic gene expression in a single cell, Science297, 1183 (2002) 2002

[2] L. S. Tsimring, Noise in biology, Reports on Progress in Physics77, 026601 (2014) 2014

[3] N. Eling, M. D. Morgan, and J. C. Marioni, Challenges in measuring and understanding biological noise, Nature Reviews Genetics20, 536 (2019) 2019

[4] M. Majka, R. Ho, and M. Zagorski, Stability of pattern formation in systems with dynamic source regions, Phys- ical Review Letters130, 098402 (2023) 2023

[5] B. Dennis and G. P. Patil, The gamma distribution and weighted multimodal gamma distributions as models of population abundance, Mathematical Biosciences68, 187 (1984) 1984

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Receipt and verification

First computed	2026-05-20T00:02:35.014923Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5e6e601b4a2c3be2e70e37a1ade21af0f5c4a7dc75cb7b59aa83fa1900361426

Aliases

arxiv: 2605.16662 · arxiv_version: 2605.16662v1 · doi: 10.48550/arxiv.2605.16662 · pith_short_12: LZXGAG2KFQ56 · pith_short_16: LZXGAG2KFQ56FZYO · pith_short_8: LZXGAG2K

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curl -sH 'Accept: application/ld+json' https://pith.science/pith/LZXGAG2KFQ56FZYOG6Q23YQ26D \
  | 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: 5e6e601b4a2c3be2e70e37a1ade21af0f5c4a7dc75cb7b59aa83fa1900361426

Canonical record JSON

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