On reflecting Brownian motion - a weak convergence approach
type: Item
instance of: scholarly article
title: On reflecting Brownian motion - a weak convergence approach
zbMATH Open document ID: 0704.60081
published in: Annales de l'Institut Henri Poincaré. Probabilités et Statistiques
publication date: 1990-01-01T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/77390
review text: Consider a d-dimensional domain D of finite Lebesgue measure. The authors define a certain sequence of stationary diffusion processes with drifts that tend to infinity at the boundary in such a way as to keep the sample paths in D. It is proved that this sequence is tight and any limit process is a continuous, stationary Markov process in \(\bar D\) that can be identified with the stationary reflecting Brownian motion defined by \textit{M. Fukushima} [see Osaka J. Math. 4, 183-215 (1967; Zbl 0317.60033)] using the Dirichlet form that is proportional to \(\int_{D}| \nabla g|^ 2 dx,\) \(g\in H^ 1(D).\) Furthermore, under a mild condition on the boundary of D, which is easily satisfied when D is a Lipschitz domain, it is shown that this process has a Skorokhod-like semimartingale representation.
Mathematics Subject Classification ID: 60J65
Mathematics Subject Classification ID: 60J60
Mathematics Subject Classification ID: 60J45
zbMATH DE Number: 4155616
zbMATH Keywords: normal reflection
zbMATH Keywords: Skorokhod representation
zbMATH Keywords: stationary reflecting Brownian motion
zbMATH Keywords: Dirichlet form
zbMATH Keywords: semimartingale representation
author: R. J. Williams
author: Weian Zheng
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4155616