The truncated Milstein method for stochastic differential equations with commutative noise

Guo, Qian and Liu, Wei and Mao, Xuerong and Yue, Rong-xian (2018) The truncated Milstein method for stochastic differential equations with commutative noise. Journal of Computational and Applied Mathematics, 338. pp. 298-310. ISSN 0377-0427

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    Abstract

    Inspired by the truncated Euler-Maruyama method developed in Mao (J. Comput. Appl. Math. 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.