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1 results

  • Quantitative Estimates for the Long-Time Behavior of an Ergodic Variant of the Telegraph Process

  • Part of
  • Joaquin Fontbona, Hélène Guérin, Florent Malrieu
  • Journal:
    Advances in Applied Probability / Volume 44 / Issue 4 / December 2012
    Published online by Cambridge University Press:
    04 January 2016, pp. 977-994
    Print publication:
    December 2012
    • Article
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  • 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.