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 …

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 …

We develop an idea of Evans and O'Connell (1994)[13], Engländer and Pinsky (1999)[10]
and Duquesne and Winkel (2007)[4] by giving a pathwise construction of the so-called …

Abstract Consider any supercritical Galton-Watson process which may become extinct with
positive probability. It is a well-understood and intuitively obvious phenomenon that, on the …

The problem of conditioning a continuous-state branching process with quadratic
competition (logistic CB process) on non-extinction is investigated. We first establish that …

We present a genealogy for superprocesses with a non-homogeneous quadratic branching
mechanism, relying on a weighted version of the superprocess introduced by Engländer and …

We prove pathwise nonuniqueness in the stochastic partial differential equations (SPDEs)
for some one-dimensional super-Brownian motions with immigration. In contrast to a closely …

Considering a random binary tree with n labelled leaves, we use a pruning procedure on
this tree in order to construct a β (3/2, 1/2)-coalescent process. We also use the continuous …

We prove the existence of the total length process for the genealogical tree of a population
model with random size given by quadratic stationary continuous-state branching …