### Distribution of the supremum location of stationary processes

**Gennady Samorodnitsky**

*(Cornell University)*

**Yi Shen**

*(Cornell University)*

#### 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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Pages: 1-17

Publication Date: June 2, 2012

DOI: 10.1214/EJP.v17-2069

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