Naslov
Positive self-similar Markov processes obtained by resurrection

Autori
Kim, Panki ; Song, Renming ; Vondraček, Zoran

Izvornik
Stochastic processes and their applications (0304-4149) 156 (2023); 379-420

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Positive self-similar Markov process ; Lamperti transform ; Lévy process ; Jump kernel ; Resurrection

Sažetak
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, ∞). 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.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA