Long time behavior of telegraph processes under convex potentials

Joaquin Fontbona (1) , Hélène Guérin (2) , Florent Malrieu (3)

1 CMM - Centre de modélisation mathématique / Centro de Modelamiento Matemático [Santiago]
2 IRMAR - Institut de Recherche Mathématique de Rennes
3 LMPT - Laboratoire de Mathématiques et Physique Théorique

We study the long-time behavior of variants of the telegraph process with position-dependent jump-rates, which result in a monotone gradient-like drift toward the origin. We compute their invariant laws and obtain, via probabilistic couplings arguments, some quantitative estimates of the total variation distance to equilibrium. Our techniques extend ideas previously developed for a simplified piecewise deterministic Markov model of bacterial chemotaxis.

Mots clés: chemotaxis models; total variation distance; telegraph process; long time behavior; Piecewise Deterministic Markov Process; coupling

Domaines: Probabilités [math.PR]

Joaquin Fontbona, Hélène Guérin, Florent Malrieu. Long time behavior of telegraph processes under convex potentials. Stochastic Processes and their Applications, 2016, 126 (10), pp.3077-3101. ⟨10.1016/j.spa.2016.04.002⟩. ⟨hal-01176036⟩