报告人：Andreas Kyprianou（University of Bath）
时间：2019-02-22 10:10-11:00
地点：Room 1303, Sciences Building No. 1
Abstract: Bañuelos and Bogdan (2004) and Bogdan, Palmowski and Wang (2016) analyse the asymptotic
tail distribution of the first time a stable (Lévy) process in dimension d\ge 2 exists a cone. We use these
results to develop the notion of a stable process conditioned to remain in a cone as well as the the notion
of a stable process conditioned to absorb continuously at the apex of a cone (without leaving the cone).
As self-similar Markov processes we examine some of their fundamental properties through the lens of
its Lamperti-Kiu decomposition. In particular we are interested to understand the underlying structure
of the Markov additive process that drives such processes. As a consequence of our interrogation of the
underlying MAP, we are able to provide an answer by example to the open question: If the modulator
of a MAP has a stationary distribution, under what conditions does its ascending ladder MAP have a
stationary distribution? We show how the two forms of conditioning are dual to one another.
Moreover, we construct the null-recurrent extension of the stable process killed on exiting a cone, showing that it again remains in the class of self-similar Markov processes.
