The truncated Milstein method for stochastic differential equations with commutative noise

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

doi:10.1016/j.cam.2018.01.014

The truncated Milstein method for stochastic differential equations with commutative noise

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

Mathematics And Statistics

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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.

Original language	English
Pages (from-to)	298-310
Number of pages	13
Journal	Journal of Computational and Applied Mathematics
Volume	338
Early online date	2 Mar 2018
DOIs	https://doi.org/10.1016/j.cam.2018.01.014
Publication status	Published - 15 Aug 2018

Keywords

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

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10.1016/j.cam.2018.01.014Licence: CC BY 4.0

Guo-etal-JCAM-2018-The-truncated-Milstein-method-for-stochastic-differential-equationsFinal published version, 378 KBLicence: CC BY 4.0

Cite this

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title = "The truncated Milstein method for stochastic differential equations with commutative noise",

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.",

keywords = "strong convergence rate, non-linear stochastic differential equations, truncated Milstein method, non-global Lipschitz condition",

author = "Qian Guo and Wei Liu and Xuerong Mao and Rong-xian Yue",

year = "2018",

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AU - Guo, Qian

AU - Liu, Wei

AU - Mao, Xuerong

AU - Yue, Rong-xian

PY - 2018/8/15

Y1 - 2018/8/15

N2 - 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.

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

UR - https://www.sciencedirect.com/science/journal/aip/03770427

U2 - 10.1016/j.cam.2018.01.014

DO - 10.1016/j.cam.2018.01.014

M3 - Article

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VL - 338

SP - 298

EP - 310

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

ER -

The truncated Milstein method for stochastic differential equations with commutative noise

Abstract

Keywords

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Long-time dynamics of numerical solutions of stochastic differential equations

Numerical Analysis of Stochastic Differential Equations: New Challenges

Cite this

The truncated Milstein method for stochastic differential equations with commutative noise

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Projects

Long-time dynamics of numerical solutions of stochastic differential equations

Numerical Analysis of Stochastic Differential Equations: New Challenges

Cite this