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April 2004 Stochastic bounds for Lévy processes
R. A. Doney
Ann. Probab. 32(2): 1545-1552 (April 2004). 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.

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R. A. Doney. "Stochastic bounds for Lévy processes." Ann. Probab. 32 (2) 1545 - 1552, April 2004. https://doi.org/10.1214/009117904000000315

Information

Published: April 2004
First available in Project Euclid: 18 May 2004

zbMATH: 1046.60045
MathSciNet: MR2060308
Digital Object Identifier: 10.1214/009117904000000315

Subjects:
Primary: 60G17 , 60G51

Keywords: exit times , processes with independent increments , Random walks , weak drift to infinity

Rights: Copyright © 2004 Institute of Mathematical Statistics

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Vol.32 • No. 2 • April 2004
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