MS-stability of the Euler-Maruyama method for stochastic differential delay equations

The aim of this paper is to investigate the stability of the Euler-Maruyama method for the stochastic differential equations with time delay. The definition of MS-stability of numerical methods is established. The condition of the mean square stability of analytical solution is obtained for a linear scalar system with multiplicative noise, and the MS-stability of the numerical scheme is proved.

[1]  Yoshihiro Saito,et al.  Stability Analysis of Numerical Schemes for Stochastic Differential Equations , 1996 .

[2]  G. Milstein.  Numerical Integration of Stochastic Differential Equations , 1994 .

[3]  E. Platen,et al.  Strong discrete time approximation of stochastic differential equations with time delay , 2000 .

[4]  X. Mao,et al.  Razumikhin-type theorems on exponential stability of stochastic functional differential equations , 1996 .

[5]  S. Mohammed.  Stochastic functional differential equations , 1984 .

[6]  Evelyn Buckwar,et al.  Introduction to the numerical analysis of stochastic delay differential equations , 2000 .

[7]  X. Mao.  Exponential stability in mean square of neutral stochastic differential functional equations , 1995 .

[8]  Kai Liu,et al.  On the exponential stability in mean square of neutral stochastic functional differential equations , 1999 .

[9]  Desmond J. Higham,et al.  Mean-Square and Asymptotic Stability of the Stochastic Theta Method , 2000, SIAM J. Numer. Anal..

[10]  K. Burrage,et al.  High strong order explicit Runge-Kutta methods for stochastic ordinary differential equations , 1996 .

[11]  P. Kloeden,et al.  Numerical Solution of Stochastic Differential Equations , 1992 .

[12]  Tianhai Tian,et al.  Two-Stage Stochastic Runge-Kutta Methods for Stochastic Differential Equations , 2002 .

[13]  X. Mao,et al.  Stochastic Differential Equations and Applications , 1998 .

[14]  X. Mao,et al.  Exponential Stability of Stochastic Di erential Equations , 1994 .