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

3 Citations (Scopus)

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

Access to Document

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

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1 Active
2 Finished

Long-time dynamics of numerical solutions of stochastic differential equations
Mao, X.
Royal Society
1/10/16 → 30/09/21
Project: Research
Ergodicity and invariant measures of stochastic delay systems driven by various noises and their applications (Prof. Fuke Wu)
Mao, X.
Royal Society
16/03/17 → 15/06/20
Project: Research Fellowship
Epsrc Doctoral Training Grant | Liang, Yanfeng
Greenhalgh, D., Mao, X. & Liang, Y.
EPSRC (Engineering and Physical Sciences Research Council)
1/10/12 → 3/10/16
Project: Research Studentship - Internally Allocated

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",

year = "2020",

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language = "English",

volume = "153",

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journal = "Applied Numerical Mathematics",

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T1 - Truncated Euler-Maruyama method for classical and time-changed non-autonomous stochastic differential equations

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

VL - 153

SP - 66

EP - 81

JO - Applied Numerical Mathematics

JF - Applied Numerical Mathematics

SN - 0168-9274

ER -

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

Abstract

Keywords

Access to Document

Long-time dynamics of numerical solutions of stochastic differential equations

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

Epsrc Doctoral Training Grant | Liang, Yanfeng

Cite this