Convergence and stability of the semi-implicit Euler method for a linear stochastic differential delay equation

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摘要

The paper deals with convergence and stability of the semi-implicit Euler method for a linear stochastic differential delay equation. It is proved that the semi-implicit Euler method is convergent with strong order p=12. The conditions under which the method is MS-stable and GMS-stable are determined and the numerical experiments are given.

论文关键词：Stochastic differential delay equations,MS-stability,GMS-stability,Semi-implicit Euler method,Numerical solution

论文评审过程：Received 10 May 2003, Revised 25 January 2004, Available online 9 April 2004.

论文官网地址：https://doi.org/10.1016/j.cam.2004.01.040