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- W2123620900 abstract "Given a Lévy process $$xi $$ , we find necessary and sufficient conditions for almost sure finiteness of the perpetual integral $$int _0^infty f(xi _s)hbox {d}s$$ , where $$f$$ is a positive locally integrable function. If $$mu =mathbb {E}[xi _1]in (0,infty )$$ and $$xi $$ has local times we prove the 0–1 law $$begin{aligned} mathbb {P}Big (int _0^infty f(xi _s),hbox {d}s<infty Big )in {0,1} end{aligned}$$ with the exact characterization $$begin{aligned} mathbb {P}Big (int _0^infty f(xi _s),hbox {d}s<infty Big )=0qquad Longleftrightarrow qquad int ^infty f(x),hbox {d}x=infty . end{aligned}$$ The proof uses spatially stationary Lévy processes, local time calculations, Jeulin’s lemma and the Hewitt–Savage 0–1 law." @default.
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- W2123620900 date "2015-03-07" @default.
- W2123620900 modified "2023-10-06" @default.
- W2123620900 title "Perpetual Integrals for Lévy Processes" @default.
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- W2123620900 doi "https://doi.org/10.1007/s10959-015-0607-y" @default.
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