Existence and uniqueness theorem of solution for stochastic differential equations driven by G-Brownian motion

Abstract

Due to the different applications of the stochstic differential equations in many areas of life, such as physics, mechanical and electrical engineering, as well as economic and finance. Many researchers have been interested in studying these equations, as they have proven in many cases that they accept unique solutions, as well as their stability in some cases according to various conditions, especially Lypschitz conditions and growth conditions with different methods. Many physical phenomena and economic and financial issues have been modeled using these equations. These studies have witnessed rapid developments recently, as some researchers have expanded them to sublinear spaces by replacing Brownian motion with G-Brownian motion and setting more precise conditions to reach very important results. In this paper we prove the existence and the uniqueness of solution for a stochastic differential equation driven by G-Brownian motion where the coefficients of the equation satisfy the weakened Hölder condition and a weakened linear growth condition.