Split-step θ-method for stochastic delay differential equations

Authors:
Wanrong Cao;Peng Hao;Zhongqiang Zhang
Affiliations:
Department of Mathematics, Southeast University, Nanjing 210096, PR China and Division of Applied Mathematics, Brown University, Providence, RI 02912, United States;Department of Mathematics, Southeast University, Nanjing 210096, PR China;Division of Applied Mathematics, Brown University, Providence, RI 02912, United States
Venue:
Applied Numerical Mathematics
Year:
2014

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Abstract

In this paper we study the mean-square stability and convergence of the split-step @q-method for stochastic differential equations with fixed time delay. Under mild assumptions, the split-step @q-method is proved to be exponentially mean-square stable and converge with strong order 1/2. Numerical examples show how mean-square stability of the split-step @q-method depends on the parameter @q and the step size h for both linear and nonlinear models.