Distribution of the supremum location of stationary processes

摘要

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.