Center Manifolds For A Class Of Delay Stochastic Differential Equations Driven By Nonlinear Noise

In this thesis,we study the center manifolds for delay stochastic differential equations driven by nonlinear noise.Firstly,we consider the Wong-Zakai approximations of delay stochastic differential equation,and prove the existence of the local center manifolds for the approximate equation.Secondly,when the stochastic equation driven by linear multiplicative noise,the existence and smoothness of the center manifolds for the original equation and the approximate equation are proved.Furthermore,the convergence between the center manifolds of the two systems is also be studied.Then,we consider the delay stochastic differential equations driven by colored noise,and by using the same argument,the existence of the local center manifolds can be obtained.Finally,when the stochastic equation driven by additive noise,the existence and smoothness of the center manifolds for the original equation and the approximate equation are proved,and based on this,the convergence between the center manifolds of the two systems is investigated.