The Annals of Applied Probability

The maximum of a random walk reflected at a general barrier

Niels Richard Hansen

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Abstract

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.

Article information

Source
Ann. Appl. Probab., Volume 16, Number 1 (2006), 15-29.

Dates
First available in Project Euclid: 6 March 2006

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1141654279

Digital Object Identifier
doi:10.1214/105051605000000610

Mathematical Reviews number (MathSciNet)
MR2209334

Zentralblatt MATH identifier
1098.60044

Subjects
Primary: 60G70: Extreme value theory; extremal processes
Secondary: 60F10: Large deviations

Keywords
Exponential change of measure global maximum nonlinear renewal theory random walk reflection structural biology

Citation

Hansen, Niels Richard. The maximum of a random walk reflected at a general barrier. Ann. Appl. Probab. 16 (2006), no. 1, 15--29. doi:10.1214/105051605000000610. https://projecteuclid.org/euclid.aoap/1141654279


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