The Study On Some Classes Of Stochastic Differential Equations Driven By G-Bownian Motions

It is well-known that stochastic differential equations can solve many practical problems easily,especially financial ones.With the development of stochastic analy-sis,stochastic differential equations are getting more and more popular.Among them,reflected stochastic differential equations and multi-valued stochastic differential equa-tions,which were introduced by Denis and Cepa respectively,have been studied exten-sively.Recently,Peng have established the fundamental theory of G-framework.For the stochastic differential equations,only by proving the existence and the uniqueness of the solutions of equations can we further study the other properties of the solutions.So the existence and the uniqueness of solutions to learning equations is very necessary.In this paper,we study the existence and the uniqueness of the solutions to three types of stochastic differential equations driven by G-Brownian motions.This paper consists of three parts.In Chapter 1,we introduce the background and preliminaries on G-expectation,G-Brownian motion and related stochastic calculus.In Chapter 2,we first focus on the multi-valued stochastic differential equations driven by G-Brownian motion with a multi-valued monotone operator.The existence and the uniqueness of the solution of such equations with Lipschitzian conditions is given.Next,we study the multi-valued stochastic differential equations driven by G-Brownian motion with a subdifferential operator.Under the Caratheodory condition,the existence and the uniqueness of solutions is proved accordingly.Finally,we give the bicontinuous modification to the solutions.In Chapter 3,we investigate the reflected stochastic differential equations driven by G-Brownian motion.Under the global Caratheodory conditions,we show the existence and uniqueness result for this kind of equation.