Perpetual Integrals for Lévy Processes

Leif Döring () and Andreas E. Kyprianou
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Leif Döring: ETH Zürich
Andreas E. Kyprianou: University of Bath

Journal of Theoretical Probability, 2016, vol. 29, issue 3, 1192-1198

Abstract: Abstract Given a Lévy process $$\xi $$ ξ , we find necessary and sufficient conditions for almost sure finiteness of the perpetual integral $$\int _0^\infty f(\xi _s)\hbox {d}s$$ ∫ 0 ∞ f ( ξ s ) d s , where $$f$$ f is a positive locally integrable function. If $$\mu =\mathbb {E}[\xi _1]\in (0,\infty )$$ μ = E [ ξ 1 ] ∈ ( 0 , ∞ ) and $$\xi $$ ξ has local times we prove the 0–1 law $$\begin{aligned} \mathbb {P}\Big (\int _0^\infty f(\xi _s)\,\hbox {d}s

Keywords: Lévy processes; Fluctuation theory; Perpetual integral; 60J25; 60J55; 60J75 (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s10959-015-0607-y

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