Eccentric behaviors of the Brownian sheet along lines
type: Item
instance of: scholarly article
title: Eccentric behaviors of the Brownian sheet along lines
zbMATH Open document ID: 1019.60047
author: Robert C. Dalang
author: Thomas Mountford
published in: The Annals of Probability
publication date: 2003-05-06T00:00:00Z
review text: The Brownian sheet is a centered, continuous Gaussian random field \(W(t),\) \(t\in \mathbb R^2\), indexed by the positive quadrant in the plane, with covariance given by \(E W(s_1,s_2)W(t_1,t_2)=(s_1\wedge t_1) (s_2\wedge t_2)\). It is one of the natural extensions of Brownian motion to higher dimensional time. Distinct excursion intervals of a Brownian motion (that correspond to fixed level) have no common endpoints. What is the situation for distinct excursion sets of Brownian bubbles in the literature, and this interesting paper examines how bubbles from fixed or random levels come into contact with each other, by examining whether or not the Brownian sheet restricted to a specific type curve can have a point of increase. The Brownian bubbles behavior was also studied in the authors' previous works.
Mathematics Subject Classification ID: 60G60
Mathematics Subject Classification ID: 28A80
Mathematics Subject Classification ID: 60G15
zbMATH DE Number: 1906053
zbMATH Keywords: Brownian sheet
zbMATH Keywords: level sets
zbMATH Keywords: points of increase
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1020107769
OpenAlex ID: W2045157430
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DOI: 10.1214/AOP/1020107769
description: scientific article; zbMATH DE number 1906053