The theory of scale functions for spectrally negative Lévy processes

S Cohen, A Kuznetsov, AE Kyprianou, V Rivero… - Lévy Matters II: Recent …, 2013 - Springer
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 …

[BOOK][B] Introductory lectures on fluctuations of Lévy processes with applications

AE Kyprianou - 2006 - books.google.com
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 …

[BOOK][B] Fluctuations of Lévy processes with applications: Introductory Lectures

AE Kyprianou - 2014 - books.google.com
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 …

[BOOK][B] Measure-Valued Branching Processes

Z Li, Z Li - 2011 - Springer
A measure-valued process describes the evolution of a population that evolves according to
the law of chance. In this chapter we provide some basic characterizations and constructions …

Fluctuations of stable processes and exponential functionals of hypergeometric Lévy processes

A Kuznetsov, JC Pardo - Acta Applicandae Mathematicae, 2013 - Springer
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 …

Coalescences in continuous-state branching processes

C Foucart, C Ma, B Mallein - 2019 - projecteuclid.org
Consider a continuous-state branching population constructed as a flow of nested
subordinators. Inverting the subordinators and reversing time give rise to a flow of …

Lamperti-type laws

LF James - 2010 - projecteuclid.org
This paper explores various distributional aspects of random variables defined as the ratio of
two independent positive random variables where one variable has an α-stable law, for 0< …

Spine representations for non-compact models of random geometry

JF Le Gall, A Riera - Probability Theory and Related Fields, 2021 - Springer
We provide a unified approach to the three main non-compact models of random geometry,
namely the Brownian plane, the infinite-volume Brownian disk, and the Brownian half-plane …

[HTML][HTML] Continuous state branching processes in random environment: the Brownian case

S Palau, JC Pardo - Stochastic Processes and their Applications, 2017 - Elsevier
We consider continuous-state branching processes that are perturbed by a Brownian
motion. These processes are constructed as the unique strong solution of a stochastic …

[HTML][HTML] Quasi-stationary distributions and Yaglom limits of self-similar Markov processes

B Haas, V Rivero - Stochastic Processes and their Applications, 2012 - Elsevier
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 …