Right inverses of nonsymmetric Lévy processes.
type: Item
instance of: scholarly article
title: Right inverses of nonsymmetric Lévy processes.
zbMATH Open document ID: 1040.60040
author: Matthias Winkel
published in: The Annals of Probability
publication date: 2003-05-06T00:00:00Z
review text: Let \(X=(X_t)_{t\geq 0}\) be a Lévy process. An increasing process \(K\) is called a right inverse of \(X\), if it satisfies \(X(K_x)=x\) for all \(x\geq 0\). \textit{S. N. Evans} [Probab. Theory Relat. Fields 118, 37--48 (2000; Zbl 0967.60060)] has characterised the symmetric Lévy processes that have right inverses. The present paper addresses the question what happens when symmetry fails. It is shown that both \(X\) and \(-X\) have right inverses if and only if \(X\) is recurrent and has a non-trivial Gaussian component. The paper also addresses the question when only \(X\) has a (partial) right inverse and gives a description of the excursion measure \(n^Z\) of the strong Markov process \(Z=X-L\) (reflected process) where \(L_t=\inf\{x>0\); \(K_x>t\}\).
reviewed by: Uwe Franz
Mathematics Subject Classification ID: 60G51
Mathematics Subject Classification ID: 60J25
Mathematics Subject Classification ID: 60J45
zbMATH DE Number: 1906056
zbMATH Keywords: Lévy processes
zbMATH Keywords: subordinators
zbMATH Keywords: excursions
zbMATH Keywords: potential theory
zbMATH Keywords: right inverses
zbMATH Keywords: creeping
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1020107772
OpenAlex ID: W2079782388
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DOI: 10.1214/AOP/1020107772
description: scientific article; zbMATH DE number 1906056