On the averaging principle for SDEs driven by G-Brownian motion with non-Lipschitz coefficients

In this paper, we aim to develop the averaging principle for stochastic differential equations driven by G-Brownian motion (G-SDEs for short) with non-Lipschitz coefficients. By the properties of G-Brownian motion and stochastic inequality, we prove that the solution of the averaged G-SDEs converges to that of the standard one in the mean-square sense and also in capacity. Finally, two examples are presented to illustrate our theory.

Automated summary

This paper develops the averaging principle for stochastic differential equations driven by G-Brownian motion with non-Lipschitz coefficients. By proving the convergence properties of the solutions, it demonstrates that the solution of the averaged G-SDEs converges to that of the standard one, and provides two examples for illustration.