Recurrent extensions of self-similar Markov processes and Cramér's condition II

Abstract

We prove that a positive self-similar Markov process $(X,\mathbb{P})$ 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.

Published in at http://dx.doi.org/10.3150/07-BEJ6082 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)

References in corpus (2)

• Recurrent extensions of self-similar Markov processes and Cramér's condition II
• Weak convergence of positive self-similar Markov processes and overshoots of Lévy processes

Cited by in corpus (6)

• Recurrent extensions of self-similar Markov processes and Cramér's condition II
• Weak convergence of positive self-similar Markov processes and overshoots of Lévy processes
• On the Lamperti stable processes
• Law of the exponential functional of a new family of one-sided Levy processes via self-similar continuous state branching processes with immigration and the Wright hypergeometric functions
• Infinite divisibility of solutions to some self-similar integro-differential equations and exponential functionals of Lévy processes
• On continuous state branching processes: conditioning and self-similarity