Stochastic averaging for non-Lipschitz multi-valued stochastic differential equations driven by G-Brownian motion

TL;DR

This paper establishes an averaging principle for multi-valued stochastic differential equations driven by G-Brownian motion with non-Lipschitz coefficients, demonstrating convergence of solutions and illustrating the theory with an example.

Contribution

It introduces a new averaging principle for non-Lipschitz MSDEs driven by G-Brownian motion, extending existing stochastic analysis methods.

Findings

Proved convergence of solutions in p-th moments and capacity.

Validated the averaging principle with a concrete example.

Abstract

In this paper, we prove the validity of an averaging principle for multi-valued stochastic differential equations (MSDEs) driven by G-Brownian motion with non-Lipschitz coefficients. The convergence theorem between the solution of the averaged MSDEs and original one was obtained in the sense of p-th moments and also in capicity. Finally, one example is presented to illustrate our theory.