Large deviations for the occupation time functional of a Poisson system of independent Brownian particles
type: Item
instance of: scholarly article
title: Large deviations for the occupation time functional of a Poisson system of independent Brownian particles
zbMATH Open document ID: 0813.60029
DOI: 10.1016/0304-4149(94)90024-8
author: Jean-Dominique Deuschel
author: Kongming Wang
published in: Stochastic Processes and their Applications
publication date: 1995-05-30T00:00:00Z
review text: The authors study the large deviations and the central limit theorem for the occupation time functional of a Poisson system of independent Brownian particles in \(\mathbb{R}^ d\). They extend the results of \textit{J. T. Cox} and \textit{D. Griffeath} for random walks [Z. Wahrscheinlichkeitstheorie Verw. Geb. 66, 543-558 (1984; Zbl 0551.60028)] and partially the results of \textit{T.-Y. Lee} [Ann. Probab. 16, No. 4, 1537-1558 (1988; Zbl 0661.60046) and ibid. 17, No. 1, 46-57 (1989; Zbl 0664.60032)] to functional spaces. The order of the large deviations remains the same, namely \(T^{1/2}\) and \(T/ \log T\) in the recurrent dimensions one and two, and \(T\) for the higher transient dimensions. Explicit expressions for the corresponding rate functions and covariance functionals are given and a specific microcanonical principle is considered. In one dimension the function-space rate function is not the standard one; thus an untypical end point is reached via a nonlinear profile.
reviewed by: Uwe Schmock
Mathematics Subject Classification ID: 60F10
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 60J65
Mathematics Subject Classification ID: 82C21
zbMATH DE Number: 691004
zbMATH Keywords: infinite particle system
zbMATH Keywords: microcanonical distribution
zbMATH Keywords: large deviations
zbMATH Keywords: central limit theorem
zbMATH Keywords: occupation time functional
MaRDI profile type: Publication
full work available at URL: 0304-4149(94)90024-8
OpenAlex ID: W1995014300
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description: scientific article; zbMATH DE number 691004