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.

Bibliographische Detailangaben
Veröffentlicht in:	Bernoulli. - International Statistical Institute and Bernoulli Society for Mathematical Statistics and Probability, 1995. - 13(2007), 4, Seite 1053-1070
1. Verfasser:	Rivero, Víctor (VerfasserIn)
Format:	Online-Aufsatz
Sprache:	English
Veröffentlicht:	2007
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


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245	1	0	\|a Recurrent Extensions of Self-Similar Markov Processes and Cramér's Condition II
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520			\|a 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.
540			\|a Copyright 2007 International Statistical Institute/Bernoulli Society
650		4	\|a Excursion theory
650		4	\|a Exponential functionals of Lévy processes
650		4	\|a Lamperti's transformation
650		4	\|a Lévy processes
650		4	\|a Self-similar Markov processes
650		4	\|a Mathematics \|x Pure mathematics \|x Probability theory \|x Random variables \|x Stochastic processes \|x Markov processes
650		4	\|a Philosophy \|x Logic \|x Logical argument \|x Counterexamples
650		4	\|a Philosophy \|x Metaphysics \|x Ontology \|x Ontological properties \|x Uniqueness
650		4	\|a Mathematics \|x Mathematical expressions \|x Mathematical functions \|x Mathematical transformations
650		4	\|a Law \|x Statutory law \|x Positive laws
650		4	\|a Philosophy \|x Logic \|x Logical topics \|x Formal logic \|x Mathematical logic \|x Mathematical set theory \|x Transfinite numbers \|x Infinity
650		4	\|a Mathematics \|x Pure mathematics \|x Probability theory \|x Random variables \|x Stochastic processes \|x Martingales
650		4	\|a Law \|x Civil law \|x Family law
650		4	\|a Behavioral sciences \|x Anthropology \|x Applied anthropology \|x Cultural anthropology \|x Cultural customs \|x Burial practices \|x Cemeteries
650		4	\|a Mathematics \|x Pure mathematics \|x Calculus \|x Differential calculus \|x Mathematical integration \|x Integration theorems \|x Fubinis theorem
650		4	\|a Mathematics \|x Pure mathematics \|x Probability theory \|x Random variables \|x Stochastic processes \|x Markov processes
650		4	\|a Philosophy \|x Logic \|x Logical argument \|x Counterexamples
650		4	\|a Philosophy \|x Metaphysics \|x Ontology \|x Ontological properties \|x Uniqueness
650		4	\|a Mathematics \|x Mathematical expressions \|x Mathematical functions \|x Mathematical transformations
650		4	\|a Law \|x Statutory law \|x Positive laws
650		4	\|a Philosophy \|x Logic \|x Logical topics \|x Formal logic \|x Mathematical logic \|x Mathematical set theory \|x Transfinite numbers \|x Infinity
650		4	\|a Mathematics \|x Pure mathematics \|x Probability theory \|x Random variables \|x Stochastic processes \|x Martingales
650		4	\|a Law \|x Civil law \|x Family law
650		4	\|a Behavioral sciences \|x Anthropology \|x Applied anthropology \|x Cultural anthropology \|x Cultural customs \|x Burial practices \|x Cemeteries
650		4	\|a Mathematics \|x Pure mathematics \|x Calculus \|x Differential calculus \|x Mathematical integration \|x Integration theorems \|x Fubinis theorem
655		4	\|a research-article
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773	1	8	\|g volume:13 \|g year:2007 \|g number:4 \|g pages:1053-1070
856	4	0	\|u https://www.jstor.org/stable/25464921 \|3 Volltext
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