Positive self-similar Markov processes obtained by resurrection

被引：2

作者：

Kima, Panki ^{[1
]}

Song, Renming ^{[2
]}

Vondracek, Zoran ^{[3
]}

机构：

[1] Seoul Natl Univ, Res Inst Math, Dept Math Sci, Seoul 08826, South Korea

[2] Univ Illinois, Dept Math, Urbana, IL 61801 USA

[3] Univ Zagreb, Fac Sci, Dept Math, Zagreb, Croatia

来源：

STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 2023年 / 156卷

基金：

新加坡国家研究基金会;

关键词：

Positive self-similar Markov process; Lamperti transform; Levy process; Jump kernel; Resurrection; STABLE LEVY PROCESSES; RECURRENT EXTENSIONS;

D O I：

10.1016/j.spa.2022.11.014

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

In this paper we study positive self-similar Markov processes obtained by (partially) resurrecting a strictly alpha-stable process at its first exit time from (0, infinity). 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. (c) 2022 Elsevier B.V. All rights reserved.

引用

页码：379 / 420

页数：42

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