In this paper, we review several results from singularly perturbed differential equations with
multiple small parameters. In addition, we develop a general conceptual framework to …

We study a class of piecewise deterministic Markov processes with state space Rd× E where
E is a finite set. The continuous component evolves according to a smooth vector field that is …

We study a Markov process with two components: the first component evolves according to
one of finitely many underlying Markovian dynamics, with a choice of dynamics that changes …

Background The recent development of single-cell transcriptomics has enabled gene
expression to be measured in individual cells instead of being population-averaged. Despite …

Stochastic gradient descent is an optimisation method that combines classical gradient
descent with random subsampling within the target functional. In this work, we introduce the …

Let $(X_t) _ {t\geq 0} $ be a continuous time Markov process on some metric space $ M, $
leaving invariant a closed subset $ M_0\subset M, $ called the {\em extinction set}. We give …

Unlike traditional books presenting stochastic processes in an academic way, this book
includes concrete applications that students will find interesting such as gambling, finance …

Given an energy potential on the Euclidian space, a piecewise deterministic Markov process
is designed to sample the corresponding Gibbs measure. In dimension one an Eyring …

We present recent results on Piecewise Deterministic Markov Processes (PDMPs), involved
in biological modeling. PDMPs, first introduced in the probabilistic literature by [30], are a …

Let E be a finite set,{Fⁱ} i∈ E a family of vector fields on ℝ d leaving positively invariant a
compact set M and having a common zero p∈ M. We consider a piecewise deterministic …