Perpetual Integrals for Lévy Processes
نویسندگان
چکیده
منابع مشابه
Perpetual Integrals for Lévy Processes
Given a Lévy process ξ , we find necessary and sufficient conditions for almost sure finiteness of the perpetual integral ∫ ∞ 0 f (ξs)ds, where f is a positive locally integrable function. If μ = E[ξ1] ∈ (0,∞) and ξ has local times we prove the 0–1 law P ( ∫ ∞ 0 f (ξs) ds < ∞ ) ∈ {0, 1} with the exact characterization P ( ∫ ∞ 0 f (ξs) ds < ∞ ) = 0 ⇐⇒ ∫ ∞ f (x) dx = ∞. The proof uses spatially s...
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ژورنال
عنوان ژورنال: Journal of Theoretical Probability
سال: 2015
ISSN: 0894-9840,1572-9230
DOI: 10.1007/s10959-015-0607-y