The Annals of Applied Probability

The maximum of a random walk reflected at a general barrier

Niels Richard Hansen

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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

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

First available in Project Euclid: 6 March 2006

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

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


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.

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