December 2012 Quantitative estimates for the long-time behavior of an ergodic variant of the telegraph process
Joaquin Fontbona, Hélène Guérin, Florent Malrieu
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Adv. in Appl. Probab. 44(4): 977-994 (December 2012). DOI: 10.1239/aap/1354716586


Motivated by stability questions on piecewise-deterministic Markov models of bacterial chemotaxis, we study the long-time behavior of a variant of the classic telegraph process having a nonconstant jump rate that induces a drift towards the origin. We compute its invariant law and show exponential ergodicity, obtaining a quantitative control of the total variation distance to equilibrium at each instant of time. These results rely on an exact description of the excursions of the process away from the origin and on the explicit construction of an original coalescent coupling for both the velocity and position. Sharpness of the obtained convergence rate is discussed.


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Joaquin Fontbona. Hélène Guérin. Florent Malrieu. "Quantitative estimates for the long-time behavior of an ergodic variant of the telegraph process." Adv. in Appl. Probab. 44 (4) 977 - 994, December 2012.


Published: December 2012
First available in Project Euclid: 5 December 2012

zbMATH: 1274.60240
MathSciNet: MR3052846
Digital Object Identifier: 10.1239/aap/1354716586

Primary: 60F17 , 60J25 , 60J75 , 93E15

Keywords: chemotaxis model , coupling , long-time behavior , piecewise-deterministic Markov process , telegraph process

Rights: Copyright © 2012 Applied Probability Trust


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Vol.44 • No. 4 • December 2012
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