非Lipschitz条件下G-Brown运动驱动的随机微分方程的数值解

doi:10.6040/j.issn.1671-9352.0.2024.439

摘要/Abstract

摘要： 针对满足非Lipschitz条件的由G-Brown运动驱动的随机微分方程,运用Euler方法构造出方程的数值解,并证明Euler数值解在均方意义下收敛于解析解。最后通过一个例子验证方法的有效性。

关键词: 随机微分方程, G-布朗运动, 非Lipschitz条件, Euler方法

Abstract: This paper investigates a stochastic differential equation driven by G-Brownian motion that satisfies non-Lipschitz conditions. Initially, the Euler method is employed to construct a numerical solution for the equation. Subsequently, the convergence of the Euler numerical solution to the analytical solution is proven in the mean-square sense. Finally, an example is provided to validate the theoretical results.

Key words: stochastic differential equations, G-Brownian motion, non-Lipschitz conditions, Euler method

中图分类号:

O241

梁飞,张丽洁. 非Lipschitz条件下G-Brown运动驱动的随机微分方程的数值解[J]. 《山东大学学报(理学版)》, 2026, 61(2): 10-19.

LIANG Fei, ZHANG Lijie. Numerical solution of stochastic differential equations driven by G-Brownian motion under non-Lipschitz conditions[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2026, 61(2): 10-19.

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