Is the location of the supremum of a stationary process nearly uniformly distributed?

Authors
Samorodnitsky, Gennady Shen, Yi
Citation
Samorodnitsky, Gennady et Shen, Yi, Is the location of the supremum of a stationary process nearly uniformly distributed?, Annals of probability , 41(5), 2013, pp. 3494-3517
Journal title
Annals of probability → ACNP
ISSN journal
00911798
Volume
41
Issue
5
Year of publication
2013
Pages
3494 - 3517
Database
ACNP
SICI code
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.