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Long time behavior of telegraph processes under convex potentials

Author

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  • Fontbona, Joaquin
  • Guérin, Hélène
  • Malrieu, Florent

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.

Suggested Citation

  • Fontbona, Joaquin & Guérin, Hélène & Malrieu, Florent, 2016. "Long time behavior of telegraph processes under convex potentials," Stochastic Processes and their Applications, Elsevier, vol. 126(10), pages 3077-3101.
    • Handle: RePEc:eee:spapps:v:126:y:2016:i:10:p:3077-3101
    DOI: 10.1016/j.spa.2016.04.002
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    References listed on IDEAS

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    1. Chafaï, Djalil & Malrieu, Florent & Paroux, Katy, 2010. "On the long time behavior of the TCP window size process," Stochastic Processes and their Applications, Elsevier, vol. 120(8), pages 1518-1534, August.
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    Cited by:

    1. De Gregorio, Alessandro & Iafrate, Francesco, 2021. "Telegraph random evolutions on a circle," Stochastic Processes and their Applications, Elsevier, vol. 141(C), pages 79-108.
    2. Nikita Ratanov, 2020. "First Crossing Times of Telegraph Processes with Jumps," Methodology and Computing in Applied Probability, Springer, vol. 22(1), pages 349-370, March.
    3. Jiang Hui & Xu Lihu & Yang Qingshan, 2024. "Functional Large Deviations for Kac–Stroock Approximation to a Class of Gaussian Processes with Application to Small Noise Diffusions," Journal of Theoretical Probability, Springer, vol. 37(4), pages 3015-3054, November.

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