具有不连续轨迹过程的指数拟遍历性
Exponential quasi-ergodicity for processes with discontinuous trajectories
AI总结：
本文针对具有灭绝性的马尔可夫过程，引入弱形式Harnack不等式，建立不同初始条件生存概率比的渐近下界，以证明拟平稳分布的指数收敛，并应用于两个不满足经典Harnack不等式的连续时间过程。
摘要：
本文探讨了对于具有灭绝性的给定马尔可夫过程，在时间渐近意义下，建立两种不同初始条件的生存概率之比的渐近下界的问题。这种比较是近期证明拟平稳分布指数收敛技术中的关键步骤。我们引入了一种弱形式的Harnack不等式作为此类比较的基本要素。该性质实际上是我们旨在证明的收敛性质的一个推论。其复杂性是我们在应用中所需的灵活性水平所付出的代价。我们在示例中展示了它如何被简单而高效地使用。作为示例，我们考虑了R^d上的两个连续时间过程，它们甚至不满足局部版本的经典Harnack不等式。第一个是分段确定性过程，而第二个是跳跃方向受限的纯跳跃过程。
英文摘要：
This paper tackles the issue of establishing a lower-bound on the asymptotic ratio of survival probabilities between two different initial conditions, asymptotically in time for a given Markov process with extinction. Such a comparison is a crucial step in recent techniques for proving exponential convergence to a quasi-stationary distribution. We introduce a weak form of the Harnack inequality as the essential ingredient for such a comparison. This property is actually a consequence of the convergence property we intend to prove. Its complexity appears as the price to pay for the level of flexibility required by our applications. We show in our illustrations how simply and efficiently it can be used nonetheless. As illustrations, we consider two continuous-time processes on R^d that do not satisfy the classical Harnack inequalities, even in a local version. The first one is a piecewise deterministic process while the second is a pure jump process with restrictions on the directions of its jumps.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
