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 …

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 study the ergodic property of a continuous-state branching process with immigration and
competition, which is an extension of the models studied by Lambert (2005, Ann. Appl …

We consider a cell population subject to a parasite infection. Cells divide at a constant rate
and, at division, share the parasites they contain between their two daughter cells. The …

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 …

We propose a general method for investigating scaling limits of finite dimensional Markov
chains to diffusions with jumps. The results of tightness, identification and convergence in …

Let $\xi=(\xi_t, t\ge 0) $ be a real-valued L\'evy process and define its associated exponential
functional as follows\[I_t (\xi):=\int_0^ t\exp\{-\xi_s\}{\rm d} s,\qquad t\ge 0.\] Motivated by …

For a Lévy process ξ=(ξt) t⩾ 0 drifting to−∞, we define the so‐called exponential functional
as follows: I ξ=∫ 0∞ e ξ tdt. Under mild conditions on ξ, we show that the following …

We study the speed of extinction of continuous state branching processes in a Lévy
environment, where the associated Lévy process oscillates. Assuming that the Lévy process …

We continue with the systematic study of the speed of extinction of continuous-state
branching processes in Lévy environments under more general branching mechanisms …