A Jump Type SDE Approach to Positive Self-Similar Markov Processes

Leif Doering (1) , Matyas Barczy (2)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires
2 Department of Applied Mathematics and Probability

We present a new approach to positive self-similar Markov processes (pssMps) by reformulating Lamperti's transformation via jump type SDEs. As applications, we give direct constructions of pssMps (re)started continuously at zero if the Lamperti transformed Levy process is spectrally negative. Our paper can be seen as a continuation of similar studies for continuous state branching processes but the approach seems to be more fruitful in the context of pssMps.

Domaines: Probabilités [math.PR]

Leif Doering, Matyas Barczy. A Jump Type SDE Approach to Positive Self-Similar Markov Processes. 2011. ⟨hal-00706811⟩