Potentials of stable processes

A. E. Kyprianou, A. R. Watson

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Abstract

For a stable process, we give an explicit formula for the potential measure of the process killed outside a bounded interval and the joint law of the overshoot, undershoot and undershoot from the maximum at exit from a bounded interval. We obtain the equivalent quantities for a stable process reflected in its infimum. The results are obtained by exploiting a simple connection with the Lamperti representation and exit problems of stable processes.
Original languageEnglish
Pages (from-to)333-343
Number of pages10
JournalSeminaire de Probabilites
VolumeXLVI
DOIs
Publication statusPublished - 2014

Keywords

  • Levy processes
  • stable processes
  • reflected stable processes
  • hitting times
  • positive self-similar Markov processes
  • Lamperti representation
  • potential measures
  • resolvent measures

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