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; …

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 his seminal work from the 1950s, William Feller classified all onedimensional diffusions
on−∞≤ a< b≤∞ in terms of their ability to access the boundary (Feller's test for explosions) …

In recent work, Chaumont et al.(2013) showed that is possible to condition a stable process
with index α∈(1, 2) to avoid the origin. Specifically, they describe a new Markov process …

In this paper we consider the problem of finding entrance laws at the origin for self-similar
Markov processes in $\mathbb {R}^ d $, killed upon hitting the origin. Under suitable …

By embedding a Markov-modulated random recurrence equation in continuous time, we
derive the Markov-modulated generalized Ornstein-Uhlenbeck process. This process turns …

This note provides a factorization of a Lévy pocess over a phase-type horizon τ given the
phase at the supremum, thereby extending the Wiener–Hopf factorization for τ exponential …

Conditioning Markov processes to avoid a domain is a classical problem that has been
studied in many settings. Ingredients for standard arguments involve the leading order tail …

In this work, we study general Dirichlet coalescents, which are a family of Ξ-coalecents
constructed from iid mass partitions, and are an extension of the symmetric coalescent. This …

Growth-fragmentation processes model the evolution of positive masses which undergo
binary divisions. The aim of this paper is twofold. First, we extend the theory of growth …