Central limit theorem for the intersection of two independent Wiener sausages
type: Item
instance of: scholarly article
title: Central limit theorem for the intersection of two independent Wiener sausages
zbMATH Open document ID: 0792.60019
DOI: 10.1007/BF01195072
author: Marc Yor
author: Sophie Weinryb
publication date: 1994-07-14T00:00:00Z
review text: \textit{J.-F. Le Gall} [Ann. Probab. 14, 1219-1244 (1986; Zbl 0621.60083)] proved that \(n^ 2\) times the volume of the intersection of two independent Wiener sausages in \(\mathbb{R}^ 3\), with radius \(1/n\), converges in \(L^ 2\), as \(n \to \infty\), towards a multiple of the intersection local time at 0, for the underlying Brownian motions. We complete this result by proving a corresponding central limit theorem.
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 60G15
zbMATH DE Number: 569008
zbMATH Keywords: independent Wiener sausages
zbMATH Keywords: Brownian motions
zbMATH Keywords: central limit theorem
MaRDI profile type: Publication
cites work: A local time analysis of intersections of Brownian paths in the plane
cites work: Q3676927
cites work: Fluctuation results for the Wiener sausage
cites work: Sur la saucisse de Wiener et les points multiples du mouvement Brownien. (On the Wiener sausage and the multiple points of Brownian motion)
cites work: Q4170004
cites work: A local time approach to the self-intersections of Brownian paths in space
cites work: Asymptotic results for independent wiener sausages. application to generalized intersection local times
cites work: Étude asymptotique par des mesures de \({\mathbb{R}}^ 3\) de saucisses de Wiener localisées
cites work: Q3799450
cites work: Q3685793
full work available at URL: https://doi.org/10.1007/bf01195072
OpenAlex ID: W1998132576
published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
description: scientific article; zbMATH DE number 569008