engleski

Positive self-similar Markov processes obtained by resurrection

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.

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

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