非线性中立型随机延迟微分方程随机θ方法的稳定性

Stability of the Stochastic Theta Method for Nonlinear Neutral Stochastic Delay Differential Equations

本文研究非线性中立型随机延迟微分方程随机θ方法的均方稳定性.在方程解析解均方稳定的条件下,证明了如下结论:当θ∈[0,1/2)时,随机θ方法对于适当小的时间步长是均方稳定的;当θ∈ [1/2,1]时,随机θ方法对于任意步长都是均方稳定的.数值结果验证了所获结论的正确性.

The paper is concerned with the mean-square （MS） stability of the stochastic theta method for nonlinear neutral stochastic delay differential equations （NSDDEs）.Under a sufficient condition of MS stability to NSDDEs,it is proved that the stochastic theta method is MS-stable for every stepsize if θ∈[1/2,1],or MS-stable for sufficiently small stepsize if θ∈[0,1/2）.Some examples to illustrate the applicability of our conclusions are presented.