On a formula on the potential operators of absorbing Lévy processes in the half space

Yozo Tamura, Hiroshi Tanaka

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

A representation of the potential operator of an absorbing Lévy process in the half space (0, ∞) × Rd - 1, d ≥ 2, is given in terms of three measures μ, over(μ, ̂) and over(μ, ̇) on [0, ∞) × Rd - 1 arising in the fluctuation theory of Lévy processes. In the case of a rotation invariant stable Lévy process, the potential kernel in the half space is computed explicitly. It will also be proved that the measure over(μ, ̂) is an excessive measure (an invariant measure under some conditions) of a Markov process, which is derived from the given Lévy process in a certain way.

Original languageEnglish
Pages (from-to)199-212
Number of pages14
JournalStochastic Processes and their Applications
Volume118
Issue number2
DOIs
Publication statusPublished - 2008 Feb 1

Keywords

  • Absorbing Lévy process
  • Fluctuation theory
  • Lévy process
  • Potential operator
  • Rotation invariant stable Lévy process

ASJC Scopus subject areas

  • Statistics and Probability
  • Modelling and Simulation
  • Applied Mathematics

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