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Course 2: Piecewise Deterministic Markov Processes,

A Piecewise deterministic Markov process (PDMP) is a stochastic process involving a deterministic motion punctuated by random jumps.

This large class of non-diffusive stochastic models was introduced in the literature by Davis in 1984.

These processes arise naturally in many application areas: biology, communication networks, reliability of complex systems for example.

From a mathematical point of view, they are simple to define but their study requires a broad spectrum of classical mathematical tools.

The aim of the course is to present simple examples of PDMP appearing in different applied frameworks and to investigate their long time behavior.

To that end, we will introduce various mathematical methods as stochastic coupling, functional inequalities, spectral analysis, Meyn-Tweedie strategy, etc. 

Since this field is very active, we will provide various open and challenging problems.

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