报告时间：**2017****年****4****月****10****日（周一）上午****9****：****00 – 12****：****00**

地点：**10****号楼****222**

报告人：**邓飞其** **华南理工大学**

题目：Stability equivalence between the analytic solutions and

Euler-Maruyama numerical solutions of neutral delayed stochastic differential equations

摘要：In this talk, the investigation on the mean square exponential stability equivalence between the analytic and Euler-Maruyama numerical solutions of the

neutral delayed stochastic differential equations (NDSDEs) via the continuous time Euler-Maruyama solutions is introduced. Firstly, with some preliminaries on basic notations and assumptions, we establish the approximation degree of the numerical solutions to the analytic one of the underlying equation under the global Lipschitz condition for the dynamics and contractive mapping condition for the neutral operator of the equation, which guarantee the existence and uniqueness of the global solution. Then we show that the analytic solution of the underlying NDSDE is exponentially stable in mean square if and only if, for some sufficiently small stepsize, the Euler-Maruyama numerical solution is exponentially stable in mean square. With such a conclusion, the mean square exponential stability of the NDSDEs can be affirmed just by the simulation approach. Finally, a constructive example is proposed to verify the theoretical result by simulation. Relatively, some analysis around the present topic will be given by remarks and some challenging problems for further works will be proposed in the conclusion section.