Limit theorem for a differential equation with a long-range random coefficient
type: Item
instance of: scholarly article
title: Limit theorem for a differential equation with a long-range random coefficient
zbMATH Open document ID: 1038.60033
author: Renaud Marty
published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris
publication date: 2004-03-15T00:00:00Z
review text: The author considers a differential equation with a small parameter \(\varepsilon\) and a centered stationary long-range Gaussian process \(m\). For instance \(m\) may be a fractional white noise with Hurst index \(H\) (\(1/2<H<1\)). It is proved that the solution of this equation converges in distribution as \(\varepsilon\) goes to zero to the solution of a stochastic differential equation driven by a fractional Brownian motion: when \(m\) is an \(H\)-fractional white noise, this fractional Brownian motion has the same Hurst index. The proof is based on the theory of rough paths that has recently been put forward by T. Lyons.
Mathematics Subject Classification ID: 60G15
Mathematics Subject Classification ID: 60H10
zbMATH DE Number: 2057080
zbMATH Keywords: fractional Brownian motion
reviewed by: Dominique Lépingle
MaRDI profile type: Publication
full work available at URL: j.crma.2003.11.010
OpenAlex ID: W2077609508
cites work: Q5560061
cites work: Stochastic analysis, rough path analysis and fractional Brownian motions.
cites work: Lévy area of Wiener processes in Banach spaces
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cites work: Differential equations driven by rough signals
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cites work: Q4301585
DOI: 10.1016/J.CRMA.2003.11.010
description: scientific article; zbMATH DE number 2057080