Positive self-similar Markov processes obtained by resurrection

Panki Kim, Renming Song, Zoran Vondraček

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)379-420
Number of pages42
JournalStochastic Processes and their Applications
StatePublished - Feb 2023


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

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation
  • Applied Mathematics


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