Victor Rivero (CIMAT)

Title: Entrance laws at the origin of self-similar Markov processes in high dimensions.

Abstract: In this talk we consider the problem of defining a self-similar Markov processes for a d-dimensional process, killed upon hitting the origin, issued from the origin, which is equivalent to finding the entrance laws at the origin for such a process. Under mild assumptions, we show the existence of an entrance law and the convergence to this law when the process is started close to the origin. We obtain an explicit description of the process started from the origin as the time reversal of the original self-similar Markov process conditioned to hit the origin. Such results rely on a fluctuation theory for Markov additive processes that we will briefly explain.