Zero white noise limit through Dirichlet forms, with application to diffusions in a random medium
type: Item
instance of: scholarly article
title: Zero white noise limit through Dirichlet forms, with application to diffusions in a random medium
zbMATH Open document ID: 0803.60076
DOI: 10.1007/BF01206232
author: P. Mathieu
publication date: 1994-10-13T00:00:00Z
review text: We study the zero white noise limit for diffusions in the continuous multidimensional medium: given a continuous function on \(\mathbb{R}^ n\), \(W\), we consider diffusions whose drift term is the gradient of \(W\) and whose diffusion coefficient is constant equal to \(\varepsilon\). We describe the asymptotics of the exit time from a domain and of the law of the process when \(\varepsilon\) tends to zero. By applying these results to a random self-similar medium \(W\) we prove limit theorems for a diffusion in a random medium. Our theorems agree with results usually proved through the large deviation principle, although, in our setup, this last tool is not available. We extend to the multidimensional case properties of diffusions in a random medium already known in one dimension.
Mathematics Subject Classification ID: 60J60
Mathematics Subject Classification ID: 60H10
Mathematics Subject Classification ID: 60F10
zbMATH DE Number: 639374
zbMATH Keywords: zero white noise limit
zbMATH Keywords: exit time
zbMATH Keywords: random self-similar medium
zbMATH Keywords: large deviation principle
zbMATH Keywords: multidimensional case
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01206232
OpenAlex ID: W1974762140
published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
description: scientific article; zbMATH DE number 639374