Distribution of the supremum location of stationary processes

2011/10/07 by Gennady Samorodnitsky, Yi Shen, Samorodnitsky, Gennady +1
Mathematics · #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1110.1605

Abstract

The location of the unique supremum of a stationary process on an interval does not need to be uniformly distributed over that interval. We describe all possible distributions of the supremum location for a broad class of such stationary processes. We show that, in the strongly mixing case, this distribution does tend to the uniform in a certain sense as the length of the interval increases to infinity.

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