The zigzag process is a piecewise deterministic Markov process which can be used in
aMCMC framework to sample from a given target distribution. We prove the convergence of …

Abstract Piecewise Deterministic Markov Processes (PDMPs) are studied in a general
framework. First, different constructions are proven to be equivalent. Second, we introduce a …

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 …

The classical Bakry-Émery calculus is extended to study, for degenerated (non-elliptic, non-
reversible, or non-diffusive) Markov processes, questions such as hypoellipticity …

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 …

Monte Carlo simulations of systems of particles such as hard spheres or soft spheres with
singular kernels can display around a phase transition prohibitively long convergence times …

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 …

We provide the spectral expansion in a weighted Hilbert space of a substantial class of
invariant non-self-adjoint and non-local Markov operators which appear in limit theorems for …

We show that the convergence of finite state space Markov chains to stationarity can often
be considerably speeded up by alternating every step of the chain with a deterministic move …