Long-time behaviour of generalised Zig-Zag process

Ninon Fétique (1, 2)

1 LMPT - Laboratoire de Mathématiques et Physique Théorique
2 FDP - Fédération de recherche Denis Poisson

We study the long-time behaviour of an extension of some recent works on bacterial chemotaxis. Indeed, we consider a d-dimensional piecewise-deterministic Markov process, d ≥ 1, that models the motion of a bacterium in presence of a chemo-attractant, with parameters depending both on the position and the velocity of the bacterium. We show that under some good assumptions on the parameters of the model, the process converges exponentially fast towards its invariant measure.

Mots clés: Piecewise-deterministic Markov process; Long time behaviour; Chemotaxis model

Domaines: Probabilités [math.PR]

Ninon Fétique. Long-time behaviour of generalised Zig-Zag process. 2017. ⟨hal-01609128v1⟩