非Lipschitz条件下G-Brown运动驱动的随机微分方程的数值解

Numerical solution of stochastic differential equations driven by G-Brownian motion under non-Lipschitz conditions

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。

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.

关键词

随机微分方程 / G-布朗运动 / 非Lipschitz条件 / Euler方法

Key words

stochastic differential equations / G-Brownian motion / non-Lipschitz conditions / Euler method

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基金资助

国家自然科学基金资助项目(42271309)

陕西省自然科学基金项目(2025JC-YBMS-083)