The truncated Milstein method for stochastic differential equations with commutative noise

Qian Guo, Wei Liu, Xuerong Mao, Rong-xian Yue

Research output: Contribution to journalArticle

6 Citations (Scopus)

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.
LanguageEnglish
Pages298-310
Number of pages13
JournalJournal of Computational and Applied Mathematics
Volume338
Early online date2 Mar 2018
DOIs
Publication statusPublished - 15 Aug 2018

Fingerprint

Euler-Maruyama Method
Strong Convergence
Stochastic Equations
Convergence Rate
Differential equations
Differential equation
Numerical Examples
Class

Keywords

  • strong convergence rate
  • non-linear stochastic differential equations
  • truncated Milstein method
  • non-global Lipschitz condition

Cite this

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The truncated Milstein method for stochastic differential equations with commutative noise. / Guo, Qian; Liu, Wei; Mao, Xuerong; Yue, Rong-xian.

In: Journal of Computational and Applied Mathematics, Vol. 338, 15.08.2018, p. 298-310.

Research output: Contribution to journalArticle

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AU - Liu, Wei

AU - Mao, Xuerong

AU - Yue, Rong-xian

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AB - 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.

KW - strong convergence rate

KW - non-linear stochastic differential equations

KW - truncated Milstein method

KW - non-global Lipschitz condition

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