电报过程遍历变体长时间行为的定量估计
概率论
2012-04-27 v2
摘要
受细菌趋化性分段确定性马尔可夫模型的稳定性问题启发，我们研究了一种经典电报过程变体的长时间行为，该变体具有非恒定跳跃率，从而诱导出指向原点的漂移。我们计算了其不变分布并证明了指数遍历性，获得了在每个时刻与平衡态的全变差距离的定量控制。这些结果依赖于对过程远离原点的偏移的精确描述，以及对速度和位置显式构造的一种原创共祖耦合。还讨论了所获收敛速率的尖锐性。
引用
@article{arxiv.1006.0982,
title = {Quantitative estimates for the long time behavior of an ergodic variant of the telegraph process},
author = {Joaquin Fontbona and Hélène Guérin and Florent Malrieu},
journal= {arXiv preprint arXiv:1006.0982},
year = {2012}
}
备注
Definitive version of former paper "Quantitative estimates for the long time behavior of a PDMP describing the movement of bacteria", now accepted in Advances in Applied Probability. Presentation changed. A diffusive scaling limit result is added. Sharpness of the long-time convergence rate is discussed. 20 pages, 3 figures