The lower envelope of positive self-similar Markov processes.

Loïc Chaumont (1) , Juan-Carlos Pardo (1)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

We establish integral tests and laws of the iterated logarithm for the lower envelope of positive self-similar Markov processes at 0 and $+\infty$. Our proofs are based on the Lamperti representation and time reversal arguments. These results extend laws of the iterated logarithm for Bessel processes due to Dvoretsky and Erdös, Motoo and Rivero.

Mots clés: Self-similar Markov process; Lévy process; Lamperti representation; last passage time; time reversal; integral test; law of the iterated logarithm

Domaines: Probabilités [math.PR]

Loïc Chaumont, Juan-Carlos Pardo. The lower envelope of positive self-similar Markov processes.. 2006. ⟨hal-00005451v2⟩