An averaging principle for stochastic differential delay equations with fractional Brownian motion
type: Item
instance of: scholarly article
title: An averaging principle for stochastic differential delay equations with fractional Brownian motion
zbMATH Open document ID: 1468.34101
DOI: 10.1155/2014/479195
author: Yong Xu
author: Bin Pei
author: Yongge Li
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: An averaging principle for a class of stochastic differential delay equations (SDDEs) driven by fractional Brownian motion (fBm) with Hurst parameter in \((1 / 2, 1)\) is considered, where stochastic integration is convolved as the path integrals. The solutions to the original SDDEs can be approximated by solutions to the corresponding averaged SDDEs in the sense of both convergence in mean square and in probability, respectively. Two examples are carried out to illustrate the proposed averaging principle.
Mathematics Subject Classification ID: 34K33
Mathematics Subject Classification ID: 34K50
Mathematics Subject Classification ID: 60H10
Mathematics Subject Classification ID: 60G22
zbMATH DE Number: 7022457
Wikidata QID: Q59038605
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/479195
OpenAlex ID: W1992367608
cites work: Stochastic averaging: An approximate method of solving random vibration problems
cites work: Q5574500
cites work: Principle of Averaging for Parabolic and Elliptic Differential Equations and for Markov Processes with Small Diffusion
cites work: The averaging method for a class of stochastic differential equations
cites work: Averaging of stochastic systems of integral-differential equations with ''Poisson noise''
cites work: Stochastic Averaging of Strongly Nonlinear Oscillators under Poisson White Noise Excitation
cites work: An averaging principle for stochastic dynamical systems with Lévy noise
cites work: FRACTIONAL WHITE NOISE CALCULUS AND APPLICATIONS TO FINANCE
cites work: Stochastic averaging principle for dynamical systems with fractional Brownian motion
cites work: Existence, uniqueness, and asymptotic behavior of mild solutions to stochastic functional differential equations in Hilbert spaces
cites work: Numerical Solutions of Stochastic Functional Differential Equations
cites work: The averaging method for stochastic differential delay equations under non-Lipschitz conditions
cites work: Stochastic Calculus for Fractional Brownian Motion and Applications
cites work: Stochastic Calculus for Fractional Brownian Motion I. Theory
cites work: Stochastic calculus for fractional Brownian motion and related processes.
cites work: Stochastic integration with respect to the fractional Brownian motion
cites work: Forward, backward and symmetric stochastic integration
cites work: Q4811448
cites work: Convergence of delay differential equations driven by fractional Brownian motion
description: scientific article; zbMATH DE number 7022457