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

Advances in Difference Equations

Juan Zhong¹  Qian Guo¹ 

[1] Department of Mathematics, Shanghai Normal University, Shanghai, China

关键词: stochastic delay differential equations;    discrete semimartingale convergence theorem;    almost sure stability;    Chebyshev method;    Runge-Kutta method;    explicit schemes;    65C30;    60H10;    65L06;   

DOI  :  10.1186/s13662-015-0642-0

学科分类：数学（综合）

来源: SpringerOpen

【 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.

【 授权许可】

CC BY