Convergence and stability of the split-step theta method for stochastic differential equations with piecewise continuous arguments

作者：

Highlights：

• We use the SST method to solve SDEPCAs with non-global Lipschitz coefficients.

• The SST method with θ∈[1/2,1] is convergent under local Lipschitz conditions.

• The SST method with θ∈(1/2,1] is stable under some conditions on the step-size.

• The SST method with θ∈(1/2+1/2λ2/λ1,1] is stable for all step-size (0<λ2<λ1).

摘要

•We use the SST method to solve SDEPCAs with non-global Lipschitz coefficients.•The SST method with θ∈[1/2,1] is convergent under local Lipschitz conditions.•The SST method with θ∈(1/2,1] is stable under some conditions on the step-size.•The SST method with θ∈(1/2+1/2λ2/λ1,1] is stable for all step-size (0<λ2<λ1).

论文关键词：60C20,60H35,65L20,Stochastic differential equations with piecewise continuous arguments,The split-step theta (SST) method,The monotone condition,Convergence of the SST method,Exponential mean square stability

论文评审过程：Received 10 July 2016, Revised 27 October 2016, Available online 30 November 2016, Version of Record 15 December 2016.

论文官网地址：https://doi.org/10.1016/j.cam.2016.11.033