Quasi-invariance properties of a class of subordinators

Max-K. von Renesse (1) , Marc Yor (2) , Lorenzo Zambotti (2)

1 Institut für Mathematik [Berlin]
2 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

We study absolute-continuity properties of a class of stochastic processes, including the gamma and the Dirichlet processes. We prove that the laws of a general class of non-linear transformations of such processes are locally equivalent to the law of the original process and we compute explicitly the associated Radon-Nikodym densities. This work unifies and generalizes to random non-linear transformations several previous results on quasi-invariance of gamma and Dirichlet processes.

Mots clés: Gamma processes; Dirichlet processes; Subordinators; Quasi-invariance

Domaines: Probabilités [math.PR]

Max-K. von Renesse, Marc Yor, Lorenzo Zambotti. Quasi-invariance properties of a class of subordinators. 2007. ⟨hal-00156099⟩