Stochastic differential equations driven by G-Brownian motion and ordinary differential equations

Abstract

In this paper, we show that the integration of a stochastic differential equations driven by G-Brownian motion in R can be reduced to the integration of an ordinary differential equations parametrized by a variable in (Ω,F). We study the sample solutions of G-SDEs by an extention of G-Itô formula. And then we also get a comparison theorem for G-SDEs and its applications.