Estimates for the difference between approximate and exact solutions to stochastic differential equations in the G-framework

TL;DR

This paper analyzes the accuracy of Euler-Maruyama approximations for stochastic differential equations driven by G-Brownian motion, providing bounds on the difference between approximate and exact solutions under non-linear growth and non-Lipschitz conditions.

Contribution

It offers new estimates for the difference between approximate and exact solutions of SDEs in the G-framework, accommodating non-linear growth and non-Lipschitz conditions.

Findings

Euler-Maruyama solutions are bounded in M^2_G.

Provided estimates for solution differences under non-linear growth.

Extended analysis to non-Lipschitz conditions in G-framework.

Abstract

This article investigates the Euler-Maruyama approximation procedure for stochastic differential equations in the framework of G-Browinian motion with non-linear growth and non-Lipschitz conditions. Subject to non-linear growth condition, it is revealed that the Euler-Maruyama approximate solutions are bounded in M^2_G.In view ofnon-linear growth and non-uniform Lipschitz conditions,we give estimates for the difference between the exact solution Z(t) and approximate solutions Zq(t) of SDEs in the framework of G-Brownia nmotion.