Stability Of Numerical Solution To Stochastic Functional Differential Equations

Stochastic Functional Differential Equations(SFDE) are widely used in various fields. Explicit solution can rarely be obtained for most of stochastic functional differential equations, so numerical methods arouse people's attention. The stability analysis of numerical solution is of great value in scientific research, so in this paper, we mainly discuss stability of numerical solution of stochastic theta method to neutral stochastic functional differential equations under polynomial growth condition. In addition, we also establish existence,uniqueness and almost sure exponent stability of the global solution for neutral stochastic functional differential equations, stability of numerical solution to stochastic functional differential equation and stochastic differential equations with variable delay.In this paper, we make full use of stochastic analysis techniques, such as: the relevant properties of stochastic integral, semi-martingale convergence theorem to proof stability of numerical solution of stochastic theta method for stochastic functional differential equations under polynomial growth condition. The main proof train of though of this paper derive from the article of Zhou S.in 2015.