The probability of exceeding a high boundary on a random time interval for a heavy-tailed random walk

Details The probability of exceeding a high boundary on a random time interval for a heavy-tailed random walk The probability of exceeding a high boundary on a random time interval for a heavy-tailed random walk

2005-08-24

arxiv.org/abs/math/0508461v1

Annals of Applied Probability 2005, Vol. 15, No. 3, 1936-1957

Mathematics

Probability

Published at http://dx.doi.org/10.1214/105051605000000269 in the Annals of Applied Probability (http://www.imstat.org/aap/) by

Scientific paper

10.1214/105051605000000269

We study the asymptotic probability that a random walk with heavy-tailed increments crosses a high boundary on a random time interval. We use new techniques to extend results of Asmussen [Ann. Appl. Probab. 8 (1998) 354-374] to completely general stopping times, uniformity of convergence over all stopping times and a wide class of nonlinear boundaries. We also give some examples and counterexamples.

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