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 …

We consider two-dimensional Lotka–Volterra systems in a fluctuating environment. Relying
on recent results on stochastic persistence and piecewise deterministic Markov processes …

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 …

We study stochastically blinking dynamical systems as in the companion paper (Part I). We
analyze the asymptotic properties of the blinking system as time goes to infinity. The …

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 …

In this article, we present a switching control approach to studying the stabilization problem
of linear Markovian switching systems. The switching signal in feedback loop is generated …

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 consider a stochastic process driven by a linear ordinary differential equation whose
right-hand side switches at exponential times between a collection of different matrices. We …