Around the 1960s a celebrated collection of papers emerged offering a number of explicit
identities for the class of isotropic Lévy stable processes in one and higher dimensions; …

The purpose of the present work is twofold. First, we develop the theory of general self-
similar growth-fragmentation processes by focusing on martingales which appear naturally …

Stable Lévy processes lie at the intersection of Lévy processes and self-similar Markov
processes. Processes in the latter class enjoy a Lamperti-type representation as the space …

We study the distribution and various properties of exponential functionals of
hypergeometric Lévy processes. We derive an explicit formula for the Mellin transform of the …

For any two-sided jum** α-stable process, where 1<α<2, we find an explicit identity for the
law of the first hitting time of the origin. This complements existing work in the symmetric …

In this paper, we study the existence of the density associated with the exponential
functional of the Lévy process ξ, I_e_q:=0^e_qe^s\,ds, where e_q is an independent …

We discuss the existence and characterization of quasi-stationary distributions and Yaglom
limits of self-similar Markov processes that reach 0 in finite time. By Yaglom limit, we mean …

In this paper we study the α-stable continuous-state branching processes (for α∈(1, 2]) and
the α-stable continuous-state branching processes conditioned never to become extinct in …

For a positive self-similar Markov process, X, we construct a local time for the random set, Θ,
of times where the process reaches its past supremum. Using this local time we describe an …

Understanding the space–time features of how a Lévy process crosses a constant barrier for
the first time, and indeed the last time, is a problem which is central to many models in …