Lévy processes are the natural continuous-time analogue of random walks and form a rich
class of stochastic processes around which a robust mathematical theory exists. Their …

Lévy processes are the natural continuous-time analogue of random walks and form a rich
class of stochastic processes around which a robust mathematical theory exists. Their …

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 …

In this work we analyse the solution to the recurrence equation M_Ψ(z+1)=-zΨ(-
z)M_Ψ(z),\quadM_Ψ(1)=1, defined on a subset of the imaginary line and where -Ψ is any …

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 …

In this paper we solve the exit problems for (reflected) spectrally negative Lévy processes,
which are exponentially killed with a killing intensity dependent on the present state of the …

Self-similar Markov trees constitute a remarkable family of random compact real trees
carrying a decoration function that is positive on the skeleton. As the terminology suggests …

For any two-sided jumping 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 …

We consider two first passage problems for stable processes, not necessarily symmetric, in
one dimension. We make use of a novel method of path censoring in order to deduce …