Entrance laws at the origin of self-similar Markov processes in $R^d$

In this talk, we consider self-similar Markov processes defined on $R^d$ without the origin, which are killed upon hitting the origin. The goal is to try to take a weak limit as $x\rightarrow0$ under mild assumptions. The process started at the origin is obtained in a unique way by conditioning the process to be continuously absorbed at the origin and then reversing time from the absorption time. The proof uses recent techniques in Markov additive process and the Lamperti-Kiu tranformation. This is joint work with Loïc Chaumont, Andreas Kyprianou and Victor Rivero.Non UBCUnreviewedAuthor affiliation: University of BathPostdoctora