滞后型分段连续随机微分方程的稳定性

本文研究了滞后型分段连续随机微分方程的解析稳定性和数值稳定性问题.首先,利用伊藤公式等方法获得了解析解均方稳定的条件,其次,对于包括均方稳定和T-稳定在内的Euler-Maruyama方法的数值稳定性问题,运用不等式技术和随机分析方法获得了一些新的结果,证明了在一定条件下,Euler-Maruyama方法既是均方稳定又是T-稳定的,推广了随机延迟微分方程的数值稳定性结论.

STABILITY OF STOCHASTIC DIFFERENTIAL EQUATIONS WITH PIECEWISE CONSTANT ARGUMENTS OF RETARDED TYPE

In this paper, analytical stability and numerical stability are both studied for stochastic differential equations with piecewise constant arguments of retarded type. First, the condition under which the analytical solutions are mean-square stable is obtained by Itô formula. Second, some new results on the numerical stability including the mean-square stability and T-stability of the Euler-Maruyama method are established by using inequality technique and stochastic analysis method. It is proved that the Euler-Maruyama method is both mean-square stable and T-stable under some suitable conditions. Our results can be seen as the generalization of the corresponding exist ones on the numerical stability of stochastic delay differential equations.