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

Wei Liu, Mohammud Foondun, Xuerong Mao

Research output: Contribution to journalArticle

4 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.

LanguageEnglish
Pages173-182
Number of pages10
JournalStatistics and Probability Letters
Volume92
Early online date6 Jun 2014
DOIs
Publication statusPublished - Sep 2014

Fingerprint

Euler-Maruyama Method
Mean Square
Stochastic Equations
Numerical Methods
Numerical Solution
Differential equation
Polynomial Decay
Polynomial
Gamma function
Exponential Stability
Estimate
Class
Numerical methods
Numerical solution
Polynomials
Stochastic differential equations

Keywords

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

Cite this

@article{7b002a75a88a4da890ad78667f7baf8c,
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 = "9",
doi = "10.1016/j.spl.2014.06.002",
language = "English",
volume = "92",
pages = "173--182",
journal = "Statistics and Probability Letters",
issn = "0167-7152",

}

Mean square polynomial stability of numerical solutions to a class of stochastic differential equations. / Liu, Wei; Foondun, Mohammud; Mao, Xuerong.

In: Statistics and Probability Letters, Vol. 92, 09.2014, p. 173-182.

Research output: Contribution to journalArticle

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 - http://www.scopus.com/inward/record.url?scp=84904630517&partnerID=8YFLogxK

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

VL - 92

SP - 173

EP - 182

JO - Statistics and Probability Letters

T2 - Statistics and Probability Letters

JF - Statistics and Probability Letters

SN - 0167-7152

ER -