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September 2013 Is the location of the supremum of a stationary process nearly uniformly distributed?
Gennady Samorodnitsky, Yi Shen
Ann. Probab. 41(5): 3494-3517 (September 2013). DOI: 10.1214/12-AOP787

Abstract

It is, perhaps, surprising that the location of the unique supremum of a stationary process on an interval can fail to be uniformly distributed over that interval. We show that this distribution is absolutely continuous in the interior of the interval and describe very specific conditions the density has to satisfy. We establish universal upper bounds on the density and demonstrate their optimality.

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Gennady Samorodnitsky. Yi Shen. "Is the location of the supremum of a stationary process nearly uniformly distributed?." Ann. Probab. 41 (5) 3494 - 3517, September 2013. https://doi.org/10.1214/12-AOP787

Information

Published: September 2013
First available in Project Euclid: 12 September 2013

zbMATH: 1291.60069
MathSciNet: MR3127889
Digital Object Identifier: 10.1214/12-AOP787

Subjects:
Primary: 60G10, 60G17

Rights: Copyright © 2013 Institute of Mathematical Statistics

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Vol.41 • No. 5 • September 2013
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