The partially truncated Euler-Maruyama method and its stability and boundedness

Qian Guo; Wei Liu; Xuerong Mao; Rongxian Yue

doi:10.1016/j.apnum.2017.01.010

The partially truncated Euler-Maruyama method and its stability and boundedness

Qian Guo, Wei Liu, Xuerong Mao, Rongxian Yue

Mathematics And Statistics

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Abstract

The partially truncated Euler–Maruyama (EM) method is proposed in this paper for highly nonlinear stochastic differential equations (SDEs). We will not only establish the finite-time strong Lr-convergence theory for the partially truncated EM method, but also demonstrate the real benefit of the method by showing that the method can preserve the asymptotic stability and boundedness of the underlying SDEs.

Original language	English
Pages (from-to)	235-251
Number of pages	17
Journal	Applied Numerical Mathematics
Volume	115
Early online date	27 Jan 2017
DOIs	https://doi.org/10.1016/j.apnum.2017.01.010
Publication status	Published - 1 May 2017

Keywords

Stochastic differential equations
local Lipschitz condition
Khasminskii-type condition
partially truncated Euler-Maruyama method
stability
boundedness

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10.1016/j.apnum.2017.01.010

Guo-etal-ANM2017-Partially-truncated-Euler-Maruyama-method-and-its-stability-and-boundednessAccepted author manuscript, 433 KBLicence: CC BY-NC-ND 4.0

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title = "The partially truncated Euler-Maruyama method and its stability and boundedness",

abstract = "The partially truncated Euler–Maruyama (EM) method is proposed in this paper for highly nonlinear stochastic differential equations (SDEs). We will not only establish the finite-time strong Lr-convergence theory for the partially truncated EM method, but also demonstrate the real benefit of the method by showing that the method can preserve the asymptotic stability and boundedness of the underlying SDEs.",

keywords = "Stochastic differential equations, local Lipschitz condition, Khasminskii-type condition, partially truncated Euler-Maruyama method, stability, boundedness",

author = "Qian Guo and Wei Liu and Xuerong Mao and Rongxian Yue",

note = "{\textcopyright} 2017 IMACS. Published by Elsevier B.V. All rights reserved. Qian Guo, Wei Liu, Xuerong Mao, Rongxian Yue, The partially truncated Euler–Maruyama method and its stability and boundedness, Applied Numerical Mathematics, Volume 115, 2017, Pages 235-251, https://doi.org/10.1016/j.apnum.2017.01.010",

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doi = "10.1016/j.apnum.2017.01.010",

language = "English",

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journal = "Applied Numerical Mathematics",

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T1 - The partially truncated Euler-Maruyama method and its stability and boundedness

AU - Guo, Qian

AU - Liu, Wei

AU - Mao, Xuerong

AU - Yue, Rongxian

N1 - © 2017 IMACS. Published by Elsevier B.V. All rights reserved. Qian Guo, Wei Liu, Xuerong Mao, Rongxian Yue, The partially truncated Euler–Maruyama method and its stability and boundedness, Applied Numerical Mathematics, Volume 115, 2017, Pages 235-251, https://doi.org/10.1016/j.apnum.2017.01.010

PY - 2017/5/1

Y1 - 2017/5/1

N2 - The partially truncated Euler–Maruyama (EM) method is proposed in this paper for highly nonlinear stochastic differential equations (SDEs). We will not only establish the finite-time strong Lr-convergence theory for the partially truncated EM method, but also demonstrate the real benefit of the method by showing that the method can preserve the asymptotic stability and boundedness of the underlying SDEs.

AB - The partially truncated Euler–Maruyama (EM) method is proposed in this paper for highly nonlinear stochastic differential equations (SDEs). We will not only establish the finite-time strong Lr-convergence theory for the partially truncated EM method, but also demonstrate the real benefit of the method by showing that the method can preserve the asymptotic stability and boundedness of the underlying SDEs.

KW - Stochastic differential equations

KW - local Lipschitz condition

KW - Khasminskii-type condition

KW - partially truncated Euler-Maruyama method

KW - stability

KW - boundedness

UR - http://www.sciencedirect.com/science/journal/01689274

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DO - 10.1016/j.apnum.2017.01.010

M3 - Article

SN - 0168-9274

VL - 115

SP - 235

EP - 251

JO - Applied Numerical Mathematics

JF - Applied Numerical Mathematics

ER -

The partially truncated Euler-Maruyama method and its stability and boundedness

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Keywords

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