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

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

2011-10-07

arxiv.org/abs/1110.1599v1

Mathematics

Probability

Scientific paper

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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