A Characterization of the Finiteness of Perpetual Integrals of Levy Processes

2019/03/09 by Kolb, Martin, Savov, Mladen · 1 citation
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1903.03792

Abstract

We derive a criterium for the almost sure finiteness of perpetual integrals of \LL processes for a class of real functions including all continuous functions and for general one-dimensional Lévy processes that drifts to plus infinity. This generalizes previous work of Döring and Kyprianou, who considered Lévy processes having a local time, leaving the general case as an open problem. It turns out, that the criterium in the general situation simplifies significantly in the situation, where the process has a local time, but we also demonstrate that in general our criterium can not be reduced. This answers an open problem posed in \citedoring.

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