Strong convergence rates of modified truncated EM method for stochastic differential equations

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摘要

Motivated by truncated Euler–Maruyama (EM) method introduced by Mao (2015), a new explicit numerical method named modified truncated Euler–Maruyama method is developed in this paper. Strong convergence rates of the given numerical scheme to the exact solutions to stochastic differential equations are investigated under given conditions in this paper. Compared with truncated EM method, the given numerical simulation strongly converges to the exact solution at fixed time T and over a time interval [0,T] under weaker sufficient conditions. Meanwhile, the convergence rates are also obtained for both cases. Two examples are provided to support our conclusions.

论文关键词:60H10,65C30,65L20,Stochastic differential equations,Local Lipschitz condition,Modified truncated Euler–Maruyama method,Strong convergence rate

论文评审过程:Received 17 January 2017, Revised 17 November 2017, Available online 2 December 2017, Version of Record 7 December 2017.

论文官网地址:https://doi.org/10.1016/j.cam.2017.11.024