Delay dependent stability of stochastic split-step θ methods for stochastic delay differential equations

作者：Hu, Peng^*; Huang, Chengming

来源：Applied Mathematics and Computation, 2018, 339: 663-674.

DOI：10.1016/j.amc.2018.07.064

• Stochastic delay differential equations
• asymptotic mean square stability
• stochastic split-step theta method
• delay dependent stability
• root locus technique

In this paper, the delay dependent asymptotic mean square stability of the stochastic split-step theta method for a scalar linear stochastic delay differential equation with real coefficients is studied. The full stability region of this method is given by using root locus technique. The necessary and sufficient condition with respect to the equation coefficients, time stepsize and method parameter theta is derived. It is proved that the stochastic split-step backward Euler can preserve the asymptotic mean square stability of the underlying system completely. In addition, the numerical stability regions of the stochastic split-step theta method and the stochastic theta method are compared with each other. At last, we validate our conclusions by numerical experiments.

• 出版日期2018-12-15
• 单位中国地质大学（北京）; 华中科技大学