Categories Solving Linear Stability Analysis Of Stochastic Differential Delay Equations ¦È Method

Stochastic differential equations (SDEs) are widely used to the fields of finance and physics,however, only part of them can be solved analytically. Stochastic delay differential equations(SDDEs) serve as models of physical processes whose time evolution depends on their past historywith noise disturbance. Due to the time delay, the SDDEs are more difficult to solve by analyticalmethods. Therefore, numerical methods are important approach to investigate the dynamics ofphysical problems modeling with SDDEs. The conclusions drawn by unstable numerical schemesare unreliable to investigate the long-time dynamical behavior, so it is important to analyze thestability of the numerical methods.In this paper, we investigate the mean-square stability of several kinds ofθmethods for linearstochastic delay differential equations, which include compositeθMilstein method, split-stepθmethod and split-stepθMilstein methods. Compared with existing methods, the methods in thispaper extend the mean-square stability regions. Amongst them, compositeθMilstein method ad-justs the stability by varying the parameter-λ. Thereafter we illustrate that the split-stepθMilsteinmethods are superior to some existing methods according to the mean-square stability.