Open Access
November 2007 Recurrent extensions of self-similar Markov processes and Cramér’s condition II
Víctor Rivero
Bernoulli 13(4): 1053-1070 (November 2007). DOI: 10.3150/07-BEJ6082

Abstract

We prove that a positive self-similar Markov process (X, ℙ) that hits 0 in a finite time admits a self-similar recurrent extension that leaves 0 continuously if and only if the underlying Lévy process satisfies Cramér’s condition.

Citation

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Víctor Rivero. "Recurrent extensions of self-similar Markov processes and Cramér’s condition II." Bernoulli 13 (4) 1053 - 1070, November 2007. https://doi.org/10.3150/07-BEJ6082

Information

Published: November 2007
First available in Project Euclid: 9 November 2007

zbMATH: 1132.60056
MathSciNet: MR2364226
Digital Object Identifier: 10.3150/07-BEJ6082

Keywords: Excursion theory , Exponential functionals of Lévy processes , Lamperti’s transformation , Lévy processes , Self-similar Markov processes

Rights: Copyright © 2007 Bernoulli Society for Mathematical Statistics and Probability

Vol.13 • No. 4 • November 2007
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