Distribution of the norm of a multidimensional Wiener process
type: Item
instance of: scholarly article
title: Distribution of the norm of a multidimensional Wiener process
zbMATH Open document ID: 0723.60100
DOI: 10.1007/BF00970825
author: Mindaugas Bloznelis
published in: Lithuanian Mathematical Journal
publication date: 1990-01-01T00:00:00Z
review text: Let B be a separable Banach space. For a B-valued Wiener process \(W_ t\) (0\(\leq t\leq 1)\) three sufficient conditions for existence of a constant c independent of Cov \(W_ 1\) (covariance) and \((B,\| \|)\) satisfying \[ P(u\leq \| W\|_{\infty}\leq u+\epsilon)\leq c\epsilon \quad (\forall u,\epsilon >0) \] are proved. They are: 1. dim B\(<\infty.\) 2. B convex, and there is \(p\geq 2\), \(\beta >0\), such that \[ \sup \{\| x+y\| /2:\;\| x\| =\| y| =1,\quad \| x-y\| \geq \epsilon,\quad x,y\in B\}\leq 1-\beta \epsilon^ p\quad (0<\epsilon <2). \] 3. \(B=\ell_ 1\) and the first entry of \(W_ 1\) is independent of the others.
Mathematics Subject Classification ID: 60J65
Mathematics Subject Classification ID: 60B05
zbMATH DE Number: 4192834
zbMATH Keywords: Banach space valued Wiener process
reviewed by: Gong Guanglu
MaRDI profile type: Publication
cites work: Q3717921
cites work: Q3216028
cites work: Q3660592
cites work: Uniform convexity and the distribution of the norm for a Gaussian measure
cites work: Potential theory on Hilbert space
description: scientific article; zbMATH DE number 4192834