The purpose of this review article is to give an up to date account of the theory and
applications of scale functions for spectrally negative Lévy processes. Our review also …

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 …

The first part of our survey [64] was published in 1985. The long time that has elapsed has
prompted us to consider the second part not only as a continuation of the first, which treates …

The main idea of the present work is to associate with a general continuous branching
process an exploration process that contains the desirable information about the …

We consider spectrally negative Lévy process and determine the joint Laplace transform of
the exit time and exit position from an interval containing the origin of the process reflected in …

In this work, we study asymptotics of the genealogy of Galton--Watson processes
conditioned on the total progeny. We consider a fixed, aperiodic and critical offspring …

Consider a completely asymmetric Lévy process which has absolutely continuous transition
probabilities. We determine the exponential decay parameter ρ and the quasistationary …

We give a review of the state of the art with regard to the theory of scale functions for
spectrally negative Lévy processes. From this we introduce a general method for generating …

We start with stochastic models of genealogies in discrete time, distinguishing models where
the population size is fixed (models of Cannings, Wright–Fisher, and Moran; compositions of …