Advances in Applied Probability
- Adv. in Appl. Probab.
- Volume 44, Number 4 (2012), 977-994.
Quantitative estimates for the long-time behavior of an ergodic variant of the telegraph process
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.
Adv. in Appl. Probab., Volume 44, Number 4 (2012), 977-994.
First available in Project Euclid: 5 December 2012
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Fontbona, Joaquin; Guérin, Hélène; Malrieu, Florent. Quantitative estimates for the long-time behavior of an ergodic variant of the telegraph process. Adv. in Appl. Probab. 44 (2012), no. 4, 977--994. doi:10.1239/aap/1354716586. https://projecteuclid.org/euclid.aap/1354716586