par Patie, Pierre 
Référence Annals of probability, 40, 2, page (765-787)
Publication Publié, 2012-03
Référence Annals of probability, 40, 2, page (765-787)
Publication Publié, 2012-03
Article révisé par les pairs
| Résumé : | Let X be a spectrally negative self-similar Markov process with 0 as an absorbing state. In this paper, we show that the distribution of the absorption time is absolutely continuous with an infinitely continuously differentiable density. We provide a power series and a contour integral representation of this density. Then, by means of probabilistic arguments, we deduce some interesting analytical properties satisfied by these functions, which include, for instance, several types of hypergeometric functions. We also give several characterizations of the Kesten's constant appearing in the study of the asymptotic tail distribution of the absorbtion time. We end the paper by detailing some known and new examples. In particular, we offer an alternative proof of the recent result obtained by Bernyk, Dalang and Peskir [Ann. Probab. 36 (2008) 1777-1789] regarding the law of the maximum of spectrally positive Lévy stable processes. © Institute of Mathematical Statistics, 2012. |
