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

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