一类随机微分方程Runge-Kutta方法的指数稳定性

Exponential stability of Runge-Kutta methods for a class of stochastic differential equations

为进一步研究随机微分方程的稳定性,给出了随机微分方程的二级Runge-Kutta方法的算法格式,研究了二级显式随机Runge-Kutta方法的均方稳定和指数稳定的条件,并证明了对于线性检验方程,均方稳定性和指数稳定性的关系.

In order to research the stability of stochastic differential equations, the two-step Runge-Kutta methods for solving these equations are presented, and the mean square stability and exponential stability conditions of the methods are discussed. The relationship between the mean square stability and exponential stability for linear test equations is also provided.