Stochastic bounds for Lévy processes

Doney, R. A. (2004) Stochastic bounds for Lévy processes. The Annals of Probability, 32 (2). pp. 1545-1552. ISSN 0091-1798

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Using the Wiener–Hopf factorization, it is shown that it is possible to bound the path of an arbitrary Lévy process above and below by the paths of two random walks. These walks have the same step distribution, but different random starting points. In principle, this allows one to deduce Lévy process versions of many known results about the large-time behavior of random walks. This is illustrated by establishing a comprehensive theorem about Lévy processes which converge to ∞ in probability.

Item Type: Article
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 60 Probability theory and stochastic processes
Depositing User: Ms Lucy van Russelt
Date Deposited: 29 Aug 2006
Last Modified: 20 Oct 2017 14:12

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