The Vector Razumikhin Type ?~? Stability For Stochastic Functional Differential Equations With Infinite Delay

Stochastic functional differential equations(SFDEs)with infinite delay are im-portant mathematical models in the fields of physics,engineering,economy and finance.Their stability are fundamental problem of SFDEs.However,delay and random disturbance often af-fect the stability of the equation.Therefore,there are important theoretical and practical value to study the stability of SFDEs with infinite delay.In this thesis,some sufficient conditions on stability for two types of SFDEs with infinite delay are given by constructing vector Lyapunov functions,using Razumikhin technique and Ito formula,which based on the idea of Razumikhin-Mao stability theorem of SFDEs.On the one hand,this thesis concerns the general decay stability for a kind of SFDEs with infinite delay.By constructing the vector Lyapunov function,using Razumikhin tech-nique,Holder inequality,Young inequality,B-D-G inequality and other analytical techniques,we obtain vector Razumikhin type theorem with general decay stability and some sufficien-t conditions on the p-th moment?? stability as well as almost sure ?? stability.Then,the numerical examples are given to illustrate the effectiveness of the results.On the other hand,we discuss the general decay stability for a family of neutral stochas-tic functional differential equations(NSFDFs)with infinite delay.By constructing the vector Lyapunov function,using Razumikhin technique,Jensen inequality,Minkowski inequality,and other analytical techniques,we establish the vector Razumikhin type theorem with general de-cay stability,and obtain some sufficient conditions on the p-th moment ?? stability and almost sure ?? stability.Then,the numerical example is given to illustrate the effectiveness of the results.