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

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

2007-11-28

arxiv.org/abs/0711.4442v1

Bernoulli 2007, Vol. 13, No. 4, 1053-1070

Mathematics

Probability

Published in at http://dx.doi.org/10.3150/07-BEJ6082 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statist

Scientific paper

10.3150/07-BEJ6082

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 L\'{e}vy process satisfies
Cram\'{e}r's condition.

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