论文标题
通过复活获得的积极的自相似马尔可夫过程
Positive self-similar Markov processes obtained by resurrection
论文作者
论文摘要
在本文中，我们研究了通过（部分）在首次退出时间从$（0，\ infty）$恢复严格的$α$稳定过程来获得的积极的自相似马尔可夫流程。我们通过使用Lamperti变换来构建这些过程。我们解释了它们的长期行为，并在有限的时间内为0提供吸收条件。如果该过程在有限的时间在0中吸收，我们给出了复发延伸的必要条件。研究复活过程的动机来自以下事实：它们的跳跃内核可能以零爆炸。我们为大量复活的稳定过程建立了尖锐的双向跳跃内核估计。
In this paper we study positive self-similar Markov processes obtained by (partially) resurrecting a strictly $α$-stable process at its first exit time from $(0,\infty)$. We construct those processes by using the Lamperti transform. We explain their long term behavior and give conditions for absorption at 0 in finite time. In case the process is absorbed at 0 in finite time, we give a necessary and sufficient condition for the existence of a recurrent extension. The motivation to study resurrected processes comes from the fact that their jump kernels may explode at zero. We establish sharp two-sided jump kernel estimates for a large class of resurrected stable processes.
