Truncated Euler-Maruyama method for classical and time-changed non-autonomous stochastic differential equations

Wei Liu; Xuerong Mao; Jingwen Tang; Yue Wu

doi:10.1016/j.apnum.2020.02.007

Truncated Euler-Maruyama method for classical and time-changed non-autonomous stochastic differential equations

Wei Liu, Xuerong Mao, Jingwen Tang, Yue Wu

Mathematics And Statistics

Research output: Contribution to journal › Article › peer-review

19 Citations (Scopus)

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Abstract

The truncated Euler-Maruyama (EM) method is proposed to approximate a class of non-autonomous stochastic differential equations (SDEs) with the Hölder continuity in the temporal variable and the super-linear growth in the state variable. The strong convergence with the convergence rate is proved. Moreover, the strong convergence of the truncated EM method for a class of highly non-linear time-changed SDEs is studied.

Original language	English
Pages (from-to)	66-81
Number of pages	16
Journal	Applied Numerical Mathematics
Volume	153
Early online date	12 Feb 2020
DOIs	https://doi.org/10.1016/j.apnum.2020.02.007
Publication status	Published - 31 Jul 2020

Keywords

truncated Euler-Maruyama method
non-autonomous stochastic differential equations
strong convergence
super linear coefficients
time-changes stochastic differential equations

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10.1016/j.apnum.2020.02.007

Liu-etal-ANM-2020-Truncated-Euler-Maruyama-method-for-classical-and-time-changedAccepted author manuscript, 448 KBLicence: CC BY-NC-ND 4.0

Ergodicity and invariant measures of stochastic delay systems driven by various noises and their applications (Prof. Fuke Wu)
Mao, X. (Principal Investigator)
Royal Society
16/03/17 → 15/06/20
Project: Research Fellowship
Long-time dynamics of numerical solutions of stochastic differential equations
Mao, X. (Principal Investigator)
Royal Society
1/10/16 → 30/09/21
Project: Research

Cite this

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title = "Truncated Euler-Maruyama method for classical and time-changed non-autonomous stochastic differential equations",

abstract = "The truncated Euler-Maruyama (EM) method is proposed to approximate a class of non-autonomous stochastic differential equations (SDEs) with the H{\"o}lder continuity in the temporal variable and the super-linear growth in the state variable. The strong convergence with the convergence rate is proved. Moreover, the strong convergence of the truncated EM method for a class of highly non-linear time-changed SDEs is studied.",

keywords = "truncated Euler-Maruyama method, non-autonomous stochastic differential equations, strong convergence, super linear coefficients, time-changes stochastic differential equations",

author = "Wei Liu and Xuerong Mao and Jingwen Tang and Yue Wu",

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day = "31",

doi = "10.1016/j.apnum.2020.02.007",

language = "English",

volume = "153",

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AU - Liu, Wei

AU - Mao, Xuerong

AU - Tang, Jingwen

AU - Wu, Yue

PY - 2020/7/31

Y1 - 2020/7/31

N2 - The truncated Euler-Maruyama (EM) method is proposed to approximate a class of non-autonomous stochastic differential equations (SDEs) with the Hölder continuity in the temporal variable and the super-linear growth in the state variable. The strong convergence with the convergence rate is proved. Moreover, the strong convergence of the truncated EM method for a class of highly non-linear time-changed SDEs is studied.

AB - The truncated Euler-Maruyama (EM) method is proposed to approximate a class of non-autonomous stochastic differential equations (SDEs) with the Hölder continuity in the temporal variable and the super-linear growth in the state variable. The strong convergence with the convergence rate is proved. Moreover, the strong convergence of the truncated EM method for a class of highly non-linear time-changed SDEs is studied.

KW - truncated Euler-Maruyama method

KW - non-autonomous stochastic differential equations

KW - strong convergence

KW - super linear coefficients

KW - time-changes stochastic differential equations

U2 - 10.1016/j.apnum.2020.02.007

DO - 10.1016/j.apnum.2020.02.007

M3 - Article

SN - 0168-9274

VL - 153

SP - 66

EP - 81

JO - Applied Numerical Mathematics

JF - Applied Numerical Mathematics

ER -

Truncated Euler-Maruyama method for classical and time-changed non-autonomous stochastic differential equations

Abstract

Keywords

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Projects

Ergodicity and invariant measures of stochastic delay systems driven by various noises and their applications (Prof. Fuke Wu)

Long-time dynamics of numerical solutions of stochastic differential equations

Cite this