Distribution of the supremum location of stationary processes

Gennady Samorodnitsky; Yi Shen

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arXiv · 1110.1605

Distribution of the supremum location of stationary processes

Gennady Samorodnitsky·Yi Shen

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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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Gennady Samorodnitsky, Yi Shen. 2011-10-07. Distribution of the supremum location of stationary processes. https://arxiv.org/abs/1110.1605

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