Regularity of the Cauchy principal value of the local times of some Lévy processes
type: Item
instance of: scholarly article
title: Regularity of the Cauchy principal value of the local times of some Lévy processes
zbMATH Open document ID: 0922.60073
DOI: 10.1016/S0007-4497(99)80013-X
author: Jean Bertoin
author: M. Emilia Caballero
published in: Bulletin des Sciences Mathématiques
publication date: 1999-10-14T00:00:00Z
review text: Roughly speaking, the Cauchy principal value of the local times of a real-valued Lévy process \(X=(X_t, t\geq 0)\) is given by \(C_t=\text{p.v. } \int^t_0 {ds\over X_s}\), \(t\geq 0\), where the notation p.v. refers to principal value. The purpose of this paper is to investigate the regularity of the Cauchy principal value \(C\) of the local times of certain Lévy processes with no negative jumps. The authors define \(C\) under the weakest possible conditions and show that this process always has continuous sample paths. Moreover, the authors specify the real numbers \(p>1\) for which \(C\) has finite \(p\)-variation.
Mathematics Subject Classification ID: 60J99
Mathematics Subject Classification ID: 60J55
Mathematics Subject Classification ID: 60G17
zbMATH DE Number: 1268641
zbMATH Keywords: Cauchy principal value of the local times
zbMATH Keywords: Lévy processes
zbMATH Keywords: \(p\)-variation
reviewed by: Zdzisław Rychlik
MaRDI profile type: Publication
cites work: Q4888858
cites work: Cauchy's principal value of local times of Lévy processes with no negative jumps via continuous branching processes
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full work available at URL: s0007-4497(99)80013-x
OpenAlex ID: W2044534605
description: scientific article; zbMATH DE number 1268641