Nondifferentiability of curves on the Brownian sheet
type: Item
instance of: scholarly article
title: Nondifferentiability of curves on the Brownian sheet
zbMATH Open document ID: 0861.60058
author: Robert C. Dalang
author: Thomas Mountford
published in: The Annals of Probability
publication date: 1997-04-22T00:00:00Z
review text: The geometry of the level sets of the Brownian sheet \(W(t,s)\), \((t,s)\in R^2\), on the nonnegative quadrant is investigated. In particular, the event ``there exists a continuous injective function \(\gamma\) from \([0,1]\) to \((0,\infty)^2\) and \(x\in(0,1)\) such that \(\gamma\) has a nonzero gradient at \(x\) and \(W(\gamma)\) is differentiable at \(x\)'' has probability \(0\).
Mathematics Subject Classification ID: 60G60
Mathematics Subject Classification ID: 60G15
zbMATH DE Number: 926208
zbMATH Keywords: Brownian sheet
zbMATH Keywords: level sets
zbMATH Keywords: nondifferentiability
reviewed by: Nikolai N. Leonenko
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1042644712
OpenAlex ID: W2048639715
cites work: The uniform dimension of the level sets of a Brownian sheet
cites work: Q3316341
cites work: Points of increase of the Brownian sheet
cites work: Geography of the level sets of the Brownian sheet
cites work: The structure of a Brownian bubble
cites work: Q3134548
cites work: Q3846616
cites work: Contours of Brownian processes with several-dimensional times
cites work: Q3908217
cites work: Q4279461
cites work: Notes on random functions
cites work: Q3997782
cites work: Q3747436
DOI: 10.1214/AOP/1042644712
description: scientific article; zbMATH DE number 926208