The truncated Milstein method for stochastic differential equations with commutative noise

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摘要

Inspired by the truncated Euler–Maruyama method developed in Mao (2015), we propose the truncated Milstein method in this paper. The strong convergence rate is proved to be close to 1 for a class of highly non-linear stochastic differential equations with commutative noise. Numerical examples are given to illustrate the theoretical results.

论文关键词：65C20,Strong convergence rate,Non-linear stochastic differential equations with commutative noise,Truncated Milstein method,Non-global Lipschitz condition

论文评审过程：Received 7 January 2016, Revised 13 January 2018, Available online 2 March 2018, Version of Record 2 March 2018.

论文官网地址：https://doi.org/10.1016/j.cam.2018.01.014