We prove that a positive self-similar Markov process (X, 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.
Publié le : 2007-11-14
Classification:
excursion theory,
exponential functionals of Lévy processes,
Lamperti’s transformation,
Lévy processes,
self-similar Markov processes
@article{1194625602,
author = {Rivero, V\'\i ctor},
title = {Recurrent extensions of self-similar Markov processes and Cram\'er's condition II},
journal = {Bernoulli},
volume = {13},
number = {1},
year = {2007},
pages = { 1053-1070},
language = {en},
url = {http://dml.mathdoc.fr/item/1194625602}
}
Rivero, Víctor. Recurrent extensions of self-similar Markov processes and Cramér’s condition II. Bernoulli, Tome 13 (2007) no. 1, pp. 1053-1070. http://gdmltest.u-ga.fr/item/1194625602/