Positive self-similar Markov processes obtained by resurrection

Autor:	Panki Kim, Renming Song, Zoran Vondraček
Jazyk:	angličtina
Rok vydání:	2022
Předmět:	Statistics and Probability Applied Mathematics Modeling and Simulation 60G18 Positive self-similar Markov process Lamperti transform Lévy process Jump kernel Resurrection Probability (math.PR) FOS: Mathematics Mathematics - Probability
Popis:	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 $(0,\infty)$. 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. Comment: Several typos corrected
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::cbc8a1a0e914674a1ecb410fa9d53169 http://arxiv.org/abs/2206.06189 Zobrazit plný text záznamu