An averaging principle for two-time-scale stochastic functional differential equations
type: Item
instance of: scholarly article
title: An averaging principle for two-time-scale stochastic functional differential equations
zbMATH Open document ID: 1442.34127
author: Fuke Wu
author: George Yin
published in: Journal of Differential Equations
publication date: 2020-04-08T00:00:00Z
review text: This paper is mainly concerned with functional diffusions with two-time scales in which the slow-varying process includes path-dependent functionals and the fast-varying process is a rapidly-changing diffusion. At first, mixed functional Itô formulas and the corresponding martingale representation are established, and an averaging principle via weak convergence methods is also developed. Finally, it is shown that the slow-varying process converges weakly to a stochastic functional differential equation whose coefficients are averages of that of the original slow-varying process w.r.t. the invariant measure of the fast-varying process.
reviewed by: Yong Kui Chang
Mathematics Subject Classification ID: 34K50
Mathematics Subject Classification ID: 34K33
Mathematics Subject Classification ID: 34K26
Mathematics Subject Classification ID: 60G44
Mathematics Subject Classification ID: 60J60
Mathematics Subject Classification ID: 92D25
zbMATH DE Number: 7188438
zbMATH Keywords: path-dependent functional
zbMATH Keywords: two-time scale
zbMATH Keywords: weak convergence
zbMATH Keywords: martingale method
zbMATH Keywords: ergodicity
zbMATH Keywords: functional Itô formula
zbMATH Keywords: stochastic functional differential equation
MaRDI profile type: Publication
full work available at URL: j.jde.2019.12.024
OpenAlex ID: W3000158197
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DOI: 10.1016/J.JDE.2019.12.024
description: scientific article; zbMATH DE number 7188438