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2006.361: Stochastic bounds for Lévy processes

2006.361: R. A. Doney (2004) Stochastic bounds for Lévy processes. The Annals of Probability, 32 (2). pp. 1545-1552. ISSN 0091-1798

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DOI: 10.1214/009117904000000315

Abstract

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 2000 > 60 Probability theory and stochastic processes
MIMS number:2006.361
Deposited By:Miss Louise Stait
Deposited On:29 August 2006

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