Recurrent Extensions of Self-Similar Markov Processes and Cramér's Condition II
We prove that a positive self-similar Markov process (X, ${\Bbb P}$ ) 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.
Veröffentlicht in: | Bernoulli. - International Statistical Institute and Bernoulli Society for Mathematical Statistics and Probability, 1995. - 13(2007), 4, Seite 1053-1070 |
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1. Verfasser: | |
Format: | Online-Aufsatz |
Sprache: | English |
Veröffentlicht: |
2007
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Zugriff auf das übergeordnete Werk: | Bernoulli |
Schlagworte: | Excursion theory Exponential functionals of Lévy processes Lamperti's transformation Lévy processes Self-similar Markov processes Mathematics Philosophy Law Behavioral sciences |
Zusammenfassung: | We prove that a positive self-similar Markov process (X, ${\Bbb P}$ ) 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. |
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ISSN: | 13507265 |