A boundary property of semimartingale reflecting Brownian motions
type: Item
instance of: scholarly article
title: A boundary property of semimartingale reflecting Brownian motions
zbMATH Open document ID: 0617.60081
DOI: 10.1007/BF01848132
author: Martin I. Reiman
author: R. J. Williams
publication date: 1988-01-01T00:00:00Z
review text: We consider a class of reflecting Brownian motions on the non-negative orthant in \({\mathbb{R}}^ K\). In the interior of the orthant, such a process behaves like Brownian motion with constant covariance matrix and drift vector. At each of the (K-1)-dimensional faces that form the boundary of the orthant, the process reflects instantaneously in a direction that is constant over the face. We give a necessary condition for the process to have a certain semimartingale decomposition, and then show that the boundary processes appearing in this decomposition do not change the set of times that the process is at the intersection of two or more faces. This boundary property plays an essential role in the derivation (performed in a separate work) of an analytical characterization of the stationary distributions of such semimartingale reflecting Brownian motions.
Mathematics Subject Classification ID: 60J65
Mathematics Subject Classification ID: 60G17
Mathematics Subject Classification ID: 60K25
zbMATH DE Number: 4001148
zbMATH Keywords: reflecting Brownian motions
zbMATH Keywords: semimartingale decomposition
zbMATH Keywords: semimartingale
zbMATH Keywords: queueing networks
MaRDI profile type: Publication
cites work: Completely- matrices
cites work: Some generalizations of positive definiteness and monotonicity
cites work: Reflected Brownian motion on an orthant
cites work: Brownian models of open queueing networks with homogeneous customer populations∗
cites work: Q3959169
cites work: Stochastic differential equations with reflecting boundary conditions
cites work: Open Queueing Networks in Heavy Traffic
published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
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description: scientific article; zbMATH DE number 4001148