Basic Theoretical Study Of Neutral Stochastic Functional Differential Equation

This thesis is based on neutral stochastic functional differential equation,which mainly focuses on the existence and uniqueness of global solution,moment estimate,and practical stability.The content of this dissertation is arranged below:In the first chapter,it mainly introduces the research background,significance,main content,innovation points of the paper and some preliminary knowledge.In the second chapter,under the condition that drift term and dissipative term satisfy the local Lipschitz condition and the neutral term satisfies the compression condition,the Lyapunov-Razumikhin theorem is used to discuss the existence and uniqueness of the global,and moment estimate.In the third chapter,when drift term and dissipative term satisfy the global Lipschitz condition and the neutral term satisfies the compression condition,the general integral Halanay inequality is established,with Lyapunov functions and stochastic analysis theorems to discuss the moment practical estimate of neutral functional differential equation.In the last chapter,summarize the article and proposes for the future research.