Hunt's hypothesis (H) and Getoor's conjecture
type: Item
instance of: scholarly article
title: Hunt's hypothesis (H) and Getoor's conjecture
zbMATH Open document ID: 0602.60063
author: Joseph Glover
author: Murali Rao
published in: The Annals of Probability
publication date: 1986-01-01T00:00:00Z
review text: For a standard process X, the Hunt hypothesis (H) is stated as follows: Every semipolar Borel set is polar. If X is symmetric relative to some \(\sigma\)-finite measure, then X satisfies (H). In the cases of Lévy processes and processes associated with non-symmetric Dirichlet spaces, some sufficient conditions for (H) are known. In this paper, the authors show that, for a standard process X and an independent subordinator T satisfying (H), the subordinated process \(X(T_ t)\) satisfies (H). In particular, by taking T as the stable process of index \(0<\alpha <1\), the Lévy process \(X^{\alpha}\) with exponent \(\Phi^{\alpha}\) satisfies (H).
Mathematics Subject Classification ID: 60J45
Mathematics Subject Classification ID: 31D05
zbMATH DE Number: 3971914
zbMATH Keywords: Hunt hypothesis
zbMATH Keywords: semipolar Borel set
zbMATH Keywords: Lévy processes
zbMATH Keywords: non-symmetric Dirichlet spaces
zbMATH Keywords: stable process
Wikidata QID: Q123138664
reviewed by: Yoichi Oshima
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1176992463
OpenAlex ID: W2001339180
DOI: 10.1214/AOP/1176992463
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description: scientific article; zbMATH DE number 3971914