Stochastic bounds for Levy processes

Details Stochastic bounds for Levy processes Stochastic bounds for Levy processes

2004-10-06

arxiv.org/abs/math/0410153v1

Annals of Probability 2004, Vol. 32, No. 2, 1545-1552

Mathematics

Probability

Published by the Institute of Mathematical Statistics (http://www.imstat.org) in the Annals of Probability (http://www.imsta

Scientific paper

10.1214/009117904000000315

Using the Wiener-Hopf factorization, it is shown that it is possible to bound the path of an arbitrary Levy 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 Levy process versions of many known results about the large-time behavior of random walks. This is illustrated by establishing a comprehensive theorem about Levy processes which converge to \infty in probability.

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