Continuity of symmetric stable processes
type: Item
instance of: scholarly article
title: Continuity of symmetric stable processes
zbMATH Open document ID: 0675.60036
DOI: 10.1016/0047-259X(89)90078-X
author: John P. Nolan
published in: Journal of Multivariate Analysis
publication date: 1989-01-01T00:00:00Z
review text: The sample path continuity of real, symmetric separable in probability p- stable processes, \(0<p<2\), on a compact metric of a pseudometric space (T,\(\tau)\) is analysed. For \(0<p<1\) necessary and sufficient conditions are obtained for a.s. path continuity, for unboundedness and for a.s. discontinuity together with boundedness in terms of stochastic integral representations of the process. In case \(1\leq p<2\) sufficient conditions for a.s. path continuity are given and some conjectures on the stable version of the Dudley-Fernique theorem are presented. In the case of continuous version of stochastic spectral representation for any p-stable process a.s. continuity at each point of T is equivalent to a.s. path continuity.
Mathematics Subject Classification ID: 60G17
Mathematics Subject Classification ID: 60H05
Mathematics Subject Classification ID: 60G05
zbMATH DE Number: 4105967
zbMATH Keywords: p-stable processes
zbMATH Keywords: path continuity
zbMATH Keywords: stochastic integral representations
zbMATH Keywords: stable version of the Dudley-Fernique theorem
zbMATH Keywords: spectral representation
MaRDI profile type: Publication
cites work: Q5512461
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description: scientific article; zbMATH DE number 4105967