Local nondeterminism and local times for stable processes
type: Item
instance of: scholarly article
title: Local nondeterminism and local times for stable processes
zbMATH Open document ID: 0659.60106
DOI: 10.1007/BF00339994
author: John P. Nolan
publication date: 1989-01-01T00:00:00Z
review text: Our main theorem gives sufficient conditions for symmetric stable processes and fields to have a jointly continuous local time. The approach is through the \(L^ p\)-representation for such processes. We develop a measure of dependence for vectors in a normed linear space and use that to analyze the probabilistic independence of the increments of a stable process. Local nondeterminism is defined for stable processes and shown to be equivalent to ``locally approximately independent increments.'' Sufficient conditions for several classes of stable processes to be local nondeterministic are given. These ideas are extended to multidimensional stable random fields and we prove existence of jointly continuous local times. The results extend most Gaussian results to their stable analogs.
Mathematics Subject Classification ID: 60J55
Mathematics Subject Classification ID: 60G17
Mathematics Subject Classification ID: 60G60
zbMATH DE Number: 4078438
zbMATH Keywords: local nondeterminism
zbMATH Keywords: stable fields
zbMATH Keywords: stable processes
zbMATH Keywords: local time
MaRDI profile type: Publication
Wikidata QID: Q57452148
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published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
description: scientific article; zbMATH DE number 4078438