Almost sure exponential stability of an explicit stochastic orthogonal Runge-Kutta-Chebyshev method for stochastic delay differential equations

摘要

Compared with Euler-Maruyama type schemes, there is a lack of studies on the stability of Runge-Kutta type methods applied to stochastic delay differential equations (SDDEs). This paper is concerned with filling this imbalance. The focus is on the almost sure exponential stability of an explicit stochastic Runge-Kutta-Chebyshev (S-ROCK) method for an Itô-type linear test equation, which is analyzed by applying the techniques based on a discrete semimartingale convergence theorem.