Markov chain approximations to symmetric diffusions
type: Item
instance of: scholarly article
title: Markov chain approximations to symmetric diffusions
zbMATH Open document ID: 0885.60065
DOI: 10.1016/S0246-0203(97)80107-0
author: Daniel W. Stroock
author: Weian Zheng
published in: Annales de l'Institut Henri Poincaré. Probabilités et Statistiques
publication date: 1998-03-31T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/77584
review text: A Markov chain approximation for diffusions associated to divergence form operators is considered. The present paper aims to the case of generators with nonsmooth coefficients, in which the identification of limits via Dirichlet forms, which is a basic tool for symmetric Markov processes from divergence form operators, is rather hard. A number of delicate estimations is given first, which leads to a discrete setting of the De Giorgi-Moser-Nash theory. Then, a concrete symmetric Markov chain approximation for symmetric diffusions is found. This approximation for diffusions is different from that in \textit{D. W. Stroock} and \textit{S. R. S. Varadhan}'s book ``Multidimensional diffusion theory'' (1979; Zbl 0426.60069), where the approximate Markov chains are time discrete, while in the present paper the approximate Markov chains are discrete in space.
Mathematics Subject Classification ID: 60J60
Mathematics Subject Classification ID: 60J10
zbMATH DE Number: 1085965
zbMATH Keywords: symmetric diffusion
zbMATH Keywords: Dirichlet form
zbMATH Keywords: De Giorgi-Moser-Nash theory
zbMATH Keywords: divergence form operator
zbMATH Keywords: Markov chain
reviewed by: Minping Qian
MaRDI profile type: Publication
Wikidata QID: Q127840638
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description: scientific article; zbMATH DE number 1085965