Explicit multiscale numerical method for super-linear slow-fast stochastic differential equations

Yuanping Cui; Xiaoyue  Li; Xuerong Mao

doi:10.1016/j.spa.2025.104653

Explicit multiscale numerical method for super-linear slow-fast stochastic differential equations

Yuanping Cui, Xiaoyue Li^*, Xuerong Mao

^*Corresponding author for this work

Mathematics And Statistics

Research output: Contribution to journal › Article › peer-review

Abstract

This manuscript is dedicated to the numerical approximation of super-linear slow–fast stochastic differential equations (SFSDEs). Borrowing the heterogeneous multiscale idea, we propose an explicit multiscale Euler–Maruyama scheme suitable for SFSDEs with locally Lipschitz coefficients using an appropriate truncation technique. By the averaging principle, we establish the strong convergence of the numerical solutions to the exact solutions in the pth moment. Additionally, under lenient conditions on the coefficients, we also furnish a strong error estimate. In conclusion, we give two illustrative examples and accompanying numerical simulations to affirm the theoretical outcomes.

Original language	English
Article number	104653
Journal	Stochastic Processes and their Applications
Volume	187
Early online date	13 Apr 2025
DOIs	https://doi.org/10.1016/j.spa.2025.104653
Publication status	E-pub ahead of print - 13 Apr 2025

Funding

Research of this author was supported by the National Natural Science Foundation of China (No. 12401216).Research of this author was supported by the National Natural Science Foundation of China (No. 12371402, 11971096), the Tianjin Municipal Natural Science Foundation (24JCZDJC00830) and the Jilin Provincial Natural Science Foundation (No. YDZJ202101ZYTS154).Research of this author was supported by the Royal Society (No. WM160014, Royal Society Wolfson Research Merit Award) and the Royal Society of Edinburgh (No. RSE1832).

Keywords

Slow-fast stochastic differential equations
Super-linearity
Explicit multiscale scheme
pth moment
strong convergence rate

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10.1016/j.spa.2025.104653

Cui-Li-Mao-2025-Explicit-multiscale-numerical-method-for-super-linear-slow-fast-stochastic-differential-equations
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Cite this

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title = "Explicit multiscale numerical method for super-linear slow-fast stochastic differential equations",

abstract = "This manuscript is dedicated to the numerical approximation of super-linear slow–fast stochastic differential equations (SFSDEs). Borrowing the heterogeneous multiscale idea, we propose an explicit multiscale Euler–Maruyama scheme suitable for SFSDEs with locally Lipschitz coefficients using an appropriate truncation technique. By the averaging principle, we establish the strong convergence of the numerical solutions to the exact solutions in the pth moment. Additionally, under lenient conditions on the coefficients, we also furnish a strong error estimate. In conclusion, we give two illustrative examples and accompanying numerical simulations to affirm the theoretical outcomes.",

keywords = "Slow-fast stochastic differential equations, Super-linearity, Explicit multiscale scheme, pth moment, strong convergence rate",

author = "Yuanping Cui and Xiaoyue Li and Xuerong Mao",

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T1 - Explicit multiscale numerical method for super-linear slow-fast stochastic differential equations

AU - Cui, Yuanping

AU - Li, Xiaoyue

AU - Mao, Xuerong

PY - 2025/4/13

Y1 - 2025/4/13

N2 - This manuscript is dedicated to the numerical approximation of super-linear slow–fast stochastic differential equations (SFSDEs). Borrowing the heterogeneous multiscale idea, we propose an explicit multiscale Euler–Maruyama scheme suitable for SFSDEs with locally Lipschitz coefficients using an appropriate truncation technique. By the averaging principle, we establish the strong convergence of the numerical solutions to the exact solutions in the pth moment. Additionally, under lenient conditions on the coefficients, we also furnish a strong error estimate. In conclusion, we give two illustrative examples and accompanying numerical simulations to affirm the theoretical outcomes.

AB - This manuscript is dedicated to the numerical approximation of super-linear slow–fast stochastic differential equations (SFSDEs). Borrowing the heterogeneous multiscale idea, we propose an explicit multiscale Euler–Maruyama scheme suitable for SFSDEs with locally Lipschitz coefficients using an appropriate truncation technique. By the averaging principle, we establish the strong convergence of the numerical solutions to the exact solutions in the pth moment. Additionally, under lenient conditions on the coefficients, we also furnish a strong error estimate. In conclusion, we give two illustrative examples and accompanying numerical simulations to affirm the theoretical outcomes.

KW - Slow-fast stochastic differential equations

KW - Super-linearity

KW - Explicit multiscale scheme

KW - pth moment

KW - strong convergence rate

U2 - 10.1016/j.spa.2025.104653

DO - 10.1016/j.spa.2025.104653

M3 - Article

SN - 0304-4149

VL - 187

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

M1 - 104653

ER -

Explicit multiscale numerical method for super-linear slow-fast stochastic differential equations

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