Recurrent extensions of self-similar Markov processes and Cramér's condition
type: Item
instance of: scholarly article
title: Recurrent extensions of self-similar Markov processes and Cramér's condition
zbMATH Open document ID: 1077.60055
author: Víctor Manuel Rivero
published in: Bernoulli
publication date: 2005-09-28T00:00:00Z
review text: Let \(\xi\) be a real-valued Lévy process that satisfies Cramér's condition, and \(X\) a self-similar Markov process associated with \(\xi\) via Lamperti's transformation. The author proves the existence of a unique excursion measure \textbf{n}, compatible with the semigroup \(X\) and such that \({\mathbf n}(X_{0+}>0)=0\). Some descriptions of the measure \textbf{n} are given. Related paper: \textit{J. Lamperti} [Z. Wahrscheinlichkeitstheorie Verw. Geb. 22, 205--225 (1972; Zbl 0274.60052)].
Mathematics Subject Classification ID: 60J25
Mathematics Subject Classification ID: 60G18
zbMATH DE Number: 2209766
zbMATH Keywords: excursion measures
zbMATH Keywords: Lévy processes
zbMATH Keywords: weak duality
reviewed by: Gheorghe Oprişan
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.3150/bj/1120591185
OpenAlex ID: W4242838960
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DOI: 10.3150/BJ/1120591185
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description: scientific article