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Convergence and stability of the semi-implicit Euler method for a linear stochastic differential delay equation
Authors:Mingzhu Liu  Wanrong Cao  Zhencheng Fan
Institution:

Department of Mathematics, Harbin Institute of Technology, Harbin 150001, PR China

Abstract: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 Image . The conditions under which the method is MS-stable and GMS-stable are determined and the numerical experiments are given.
Keywords:Stochastic differential delay equations  MS-stability  GMS-stability  Semi-implicit Euler method  Numerical solution
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