Long time behavior of telegraph processes under convex potentials

Joaquin Fontbona, Hélène Guérin and Florent Malrieu

Stochastic Processes and their Applications, 2016, vol. 126, issue 10, 3077-3101

Abstract: 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 towards 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.

Keywords: Piecewise Deterministic Markov Process; Coupling; Long time behavior; Telegraph process; Chemotaxis models; Total variation distance (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (3)

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DOI: 10.1016/j.spa.2016.04.002

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