Stability of Exponential Euler Method for Linear Stochastic Delay Differential Equations
The main purpose of this paper is to investigate the exponential stability in mean square of the exponential Euler method to linear stochastic delay differential equations (LSDDEs).The classical stability theorem to LSDDEs is given by the Lyapunov functions.However, in this paper we study the exponential stability in mean square of the exact solution to LSDDEs by using the definition of logarithmic norm.On the other hand, the implicit Euler scheme to LSDDEs is known to be exponentially stable in mean square for any step size.However, in this article we propose an explicit method to show that the exponential Euler method to LSDDEs is proved to share the same stability for any step size by the property of logarithmic norm.
Stochastic delay differential equation Exponential euler method Lipschitz condition It^o formula Strong convergence
Ling ZHANG Guo-qing LIU
Mathematical Department of Teacher Education Institute, Daqing Normal University, Daqing,163712, P.R.China
国际会议
上海
英文
139-144
2018-04-15（万方平台首次上网日期，不代表论文的发表时间）