Lévy processes, generalized moments and uniform integrability

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Abstract

We give new proofs of certain equivalent conditions for the existence of generalized moments of a Lévy process (Xt)t≥0; in particular, the existence of a generalized g-moment is equivalent to the uniform integrabil-ity of (g(Xt))t[0,1] . As a consequence, certain functions of a Lévy process which are integrable and local martingales are already true martingales. Our methods extend to moments of stochastically continuous additive processes, and we give new, short proofs for the characterization of lattice distributions and the transience of Lévy processes.

Details

Original languageEnglish
Pages (from-to)109-131
Number of pages23
JournalProbability and Mathematical Statistics
Volume42
Issue number1
Publication statusPublished - 2022
Peer-reviewedYes

Keywords

ASJC Scopus subject areas

Keywords

  • additive process, condition D, condition DL, Dynkin’s formula, generalized moment, Gronwall’s inequality, local martingale, Lévy process

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