Long time behavior of telegraph processes under convex potentials

Joaquin Fontbona, Hélène Guérin, Florent Malrieu

Published 2015-07-13Version 1

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.