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 …

This course concerns the stochastic modeling of population dynamics. In the first part, we
focus on monotype populations described by one-dimensional stochastic differential …

The intent of this monograph is to introduce graduate students to branching process
applications of populations and epidemics. Deterministic models of populations and …

We propose and investigate a market model for power prices, including most basic features
exhibited by previous models and taking into account self-exciting properties. The model …

In this paper, we introduce branching processes in a Lévy random environment. In order to
define this class of processes, we study a particular class of non-negative stochastic …

Let (Z n) be a supercritical branching process with immigration in a random environment.
Firstly, we prove that under a simple log moment condition on the offspring and immigration …

A general continuous-state branching processes in random environment (CBRE-process) is
defined as the strong solution of a stochastic integral equation. The environment is …

; We establish a general sufficient condition for a sequence of Galton-Watson branching
processes in varying environments to converge weakly. This condition extends previous …

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 …

The asymptotic behavior of expectations of some exponential functionals of a Lévy process
is studied. The key point is the observation that the asymptotics only depend on the sample …