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Asymptotics for the First Passage Times of Lévy Processes and Random Walks
Published online by Cambridge University Press: 30 January 2018
Abstract
We study the exact asymptotics for the distribution of the first time, τx, a Lévy process Xt crosses a fixed negative level -x. We prove that ℙ{τx >t} ~V(x) ℙ{Xt≥0}/t as t→∞ for a certain function V(x). Using known results for the large deviations of random walks, we obtain asymptotics for ℙ{τx>t} explicitly in both light- and heavy-tailed cases.
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- Copyright © Applied Probability Trust 2013
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