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 …

We consider non‐conservative positive semigroups and obtain necessary and sufficient
conditions for uniform exponential contraction in weighted total variation norm. This ensures …

We give a short overview of recent results on a specific class of Markov process: the
Piecewise Deterministic Markov Processes (PDMPs). We first recall the definition of these …

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 provide quantitative bounds for the long time behavior of a class of Piecewise
Deterministic Markov Processes with state space R^d*E where E is a finite set. The …

In this note, we present few examples of Piecewise Deterministic Markov Processes and
their long time behavior. They share two important features: they are related to concrete …

We study the long-time behavior of the growth-fragmentation equation, a nonlocal linear
evolution equation describing a wide range of phenomena in structured population …

Motivated by a model for neural networks with adaptation and fatigue, we study a
conservative fragmentation equation that describes the density probability of neurons with …

The growth-fragmentation equation describes a system of growing and dividing particles,
and arises in models of cell division, protein polymerisation and even telecommunications …

The chemical master equation and its continuum approximations are indispensable tools in
the modeling of chemical reaction networks. These are routinely used to capture complex …