随机延迟微分方程SST方法的稳定性

Stability of SST method for stochastic delay differential equations

在延迟随机微分方程领域,随机分步theta(SST)数值方法的应用成果较少。研究随机分步theta(SST)方法应用于随机延迟微分方程(SDDEs)时的稳定性性质,给出在线性增长条件及单边Lipschitz条件下,SST数值解能保持原方程真实解几乎必然指数稳定的一个充分条件。数值模拟验证了所得结果的正确性及有效性。

Given little literature on stochastic split-step theta （SST） method in stochastic delay dif- ferential equations （ SDDEs）, this study will focus on the numerical stability of SST method for SDDEs. Sufficient condition under which SST method can reproduce the almost sure exponential stability of the ex- act solutions to stochastic delay differential equations are investigated with given linear growth condition and one-side Lipschitz condition. The numerical experiment confirms the correctness of the obtained theo- rem.