Strong predictor-corrector approximation for stochastic delay differential equations

Abstract

This paper presents a strong predictor-corrector method for the numerical solution of stochastic delay differential equations (SDDEs) of Ito-type. The method is proved to be mean-square convergent of order min{1/2,p} under the Lipschitz condition and the linear growth condition, where p is the exponent of Holder condition of the initial function. Stability criteria for this type of method are derived. It is shown that for certain choices of the flexible parameter p the derived method can have a better stability property than more commonly used numerical methods. That is, for some p, the asymptotic MS-stability bound of the method will be much larger than that of the Euler-Maruyama method. Numerical results are reported confirming convergence properties and comparing stability properties of methods with different parameters p. Finally, the vectorised simulation is discussed and it is shown that this implementation is much more efficient.