Konferenzvortragsdetails

Konferenz: Journées Cartes


Excursion theory for Markov processes indexed by Lévy trees

Vortrag von Alejandro Rosales Ortiz
Datum: 12.06.23   Zeit: 13.30 - 14.30   Raum: Y27H28

We introduce the notion of a Markov process indexed by a Lévy tree. This family of universal objects are intimately related to the theory of super-processes and appear in numerous limit theorems. More recently, Brownian motion indexed by the Brownian tree has played an essential role in the development of Brownian geometry. The goal of this talk is to discuss the recent development of an excursion theory for Markov processes indexed by Lévy trees. In particular, we will explain how one can introduce a notion of local time in this tree-indexed setting. Our results complement the theory developed by Abraham and Le Gall concerning Brownian motion indexed by the Brownian tree. We will assume no prerequisites other than basic properties of Brownian motion and will begin with a concise introduction to excursion theory for time-indexed Markov processes and Lévy trees. The content of this talk is based on two joint works with Armand Riera.