Mean square polynomial stability of numerical solutions to a class of stochastic differential equations

Wei Liu; Mohammud Foondun; Xuerong Mao

doi:10.1016/j.spl.2014.06.002

Mean square polynomial stability of numerical solutions to a class of stochastic differential equations

Wei Liu^*, Mohammud Foondun, Xuerong Mao

^*Corresponding author for this work

Mathematics And Statistics

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

9 Citations (Scopus)

Abstract

The exponential stability of numerical methods to stochastic differential equations (SDEs) has been widely studied. In contrast, there are relatively few works on polynomial stability of numerical methods. In this letter, we address the question of reproducing the polynomial decay of a class of SDEs using the Euler-Maruyama method and the backward Euler-Maruyama method. The key technical contribution is based on various estimates involving the gamma function.

Original language	English
Pages (from-to)	173-182
Number of pages	10
Journal	Statistics and Probability Letters
Volume	92
Early online date	6 Jun 2014
DOIs	https://doi.org/10.1016/j.spl.2014.06.002
Publication status	Published - Sept 2014

Keywords

Euler-type method
gamma function
nonlinear SDEs
numerical reproduction
polynomial stability

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10.1016/j.spl.2014.06.002

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title = "Mean square polynomial stability of numerical solutions to a class of stochastic differential equations",

abstract = "The exponential stability of numerical methods to stochastic differential equations (SDEs) has been widely studied. In contrast, there are relatively few works on polynomial stability of numerical methods. In this letter, we address the question of reproducing the polynomial decay of a class of SDEs using the Euler-Maruyama method and the backward Euler-Maruyama method. The key technical contribution is based on various estimates involving the gamma function.",

keywords = "Euler-type method, gamma function, nonlinear SDEs, numerical reproduction, polynomial stability",

author = "Wei Liu and Mohammud Foondun and Xuerong Mao",

year = "2014",

month = sep,

doi = "10.1016/j.spl.2014.06.002",

language = "English",

volume = "92",

pages = "173--182",

journal = "Statistics and Probability Letters",

issn = "0167-7152",

publisher = "Elsevier B.V.",

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TY - JOUR

T1 - Mean square polynomial stability of numerical solutions to a class of stochastic differential equations

AU - Liu, Wei

AU - Foondun, Mohammud

AU - Mao, Xuerong

PY - 2014/9

Y1 - 2014/9

N2 - The exponential stability of numerical methods to stochastic differential equations (SDEs) has been widely studied. In contrast, there are relatively few works on polynomial stability of numerical methods. In this letter, we address the question of reproducing the polynomial decay of a class of SDEs using the Euler-Maruyama method and the backward Euler-Maruyama method. The key technical contribution is based on various estimates involving the gamma function.

AB - The exponential stability of numerical methods to stochastic differential equations (SDEs) has been widely studied. In contrast, there are relatively few works on polynomial stability of numerical methods. In this letter, we address the question of reproducing the polynomial decay of a class of SDEs using the Euler-Maruyama method and the backward Euler-Maruyama method. The key technical contribution is based on various estimates involving the gamma function.

KW - Euler-type method

KW - gamma function

KW - nonlinear SDEs

KW - numerical reproduction

KW - polynomial stability

UR - https://www.scopus.com/pages/publications/84904630517

UR - http://www.sciencedirect.com/science/journal/01677152

U2 - 10.1016/j.spl.2014.06.002

DO - 10.1016/j.spl.2014.06.002

M3 - Article

AN - SCOPUS:84904630517

SN - 0167-7152

VL - 92

SP - 173

EP - 182

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

ER -

Mean square polynomial stability of numerical solutions to a class of stochastic differential equations

Abstract

Keywords

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