The maximum of a random walk reflected at a general barrier

Details The maximum of a random walk reflected at a general barrier The maximum of a random walk reflected at a general barrier

2006-03-09

arxiv.org/abs/math/0603208v1

Annals of Applied Probability 2006, Vol. 16, No. 1, 15-29

Mathematics

Probability

Published at http://dx.doi.org/10.1214/105051605000000610 in the Annals of Applied Probability (http://www.imstat.org/aap/) by

Scientific paper

10.1214/105051605000000610

We define the reflection of a random walk at a general barrier and derive, in case the increments are light tailed and have negative mean, a necessary and sufficient criterion for the global maximum of the reflected process to be finite a.s. If it is finite a.s., we show that the tail of the distribution of the global maximum decays exponentially fast and derive the precise rate of decay. Finally, we discuss an example from structural biology that motivated the interest in the reflection at a general barrier.

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