Strong convergence of implicit numerical methods for nonlinear stochastic functional differential equations

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摘要

The main aim of this work is to prove that the backward Euler–Maruyama approximate solutions converge strongly to the true solutions for stochastic functional differential equations with superlinear growth coefficients. The paper also gives the boundedness and mean-square exponential stability of the exact solutions, and shows that the backward Euler–Maruyama method can preserve the boundedness of mean-square moments. Finally, a highly nonlinear example is provided to illustrate the main results.

论文关键词:65C30,Stochastic functional differential equation,Polynomial growth condition,Backward Euler–Maruyama method,Strong convergence,Boundedness

论文评审过程:Received 3 August 2015, Revised 9 March 2017, Available online 20 April 2017, Version of Record 13 May 2017.

论文官网地址:https://doi.org/10.1016/j.cam.2017.04.015