Piecewise Deterministic Markov Processes

Abstract

A Piecewise Deterministic Markov Process (PDMP) is defined by a (finite) family of deterministic dynamical systems (usually ordinary differential equations) and a random clock. The system follows a given dynamic, and when the clock rings, it switches to another dynamic, randomly chosen. This type of process naturally appears in several fields (population dynamics, cell biology, computer science, etc.) where the system's evolution is deterministic but depends on an environment subject to random fluctuations. The qualitative analysis of the long-term behavior of PDMPs has been the focus of much attention over the last decade. In this talk, I will offer a general introduction to the subject, illustrate my points with several examples, and present the main results obtained — in collaboration with several researchers — over the past ten years.