Random fractals determined by Lévy processes
type: Item
instance of: scholarly article
title: Random fractals determined by Lévy processes
zbMATH Open document ID: 1217.60037
author: Jamison Wolf
published in: Journal of Theoretical Probability
publication date: 2011-01-07T00:00:00Z
review text: The paper is devoted to various results on Blumenthal-Getoor indices, in particular, it contains a good survey of existing results. A new index \(\eta\) for a Lévy process \(X\) is introduced, \[ \eta:=\sup\Big\{ \alpha>0: \limsup_{a\to 0} a^\alpha ET(a,a)<\infty \Big\}, \] where \(T(a,s)\) is the sojourn time of \(X\) in the ball of radius \(a\), centered at the origin, up to time \(s\). In particular, it is shown that \(\eta\) is equal to the dimension of the graph of \(X\), \(\text{Gr}(X, \mathbb R_+):=\{(t,X(t)): t\in \mathbb R_+\}\).
Mathematics Subject Classification ID: 60G51
Mathematics Subject Classification ID: 60G17
Mathematics Subject Classification ID: 28A80
zbMATH DE Number: 5833864
zbMATH Keywords: Lévy process
zbMATH Keywords: Hausdorff dimension
zbMATH Keywords: Blumenthal-Getoor indices
zbMATH Keywords: \(p\)-variation
reviewed by: V. Knopova
MaRDI profile type: Publication
full work available at URL: s10959-009-0224-8
OpenAlex ID: W1974590695
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DOI: 10.1007/S10959-009-0224-8
description: scientific article; zbMATH DE number 5833864