电报过程的一个遍历变体的长时间行为的定量估计
Quantitative estimates for the long time behavior of an ergodic variant of the telegraph process
摘要：
出于对细菌趋化性的分段确定性马尔可夫模型的稳定性问题，我们研究了经典电报过程的一个变体的长时间行为，该变体具有非恒定的跳跃率，导致向原点漂移。我们计算它的不变定律，并显示指数遍历性，获得一个定量控制的全变差距离平衡在每个时刻。这些结果依赖于一个精确的描述的过程中远离原点和明确的建设一个原始的聚结耦合的速度和位置的偏移。讨论了所得到的收敛速度的渐近性。
英文摘要：
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 non-constant 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 velocity and position. Sharpness of the obtained convergence rate is discussed.
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