Distribution of the supremum location of stationary processes
Samorodnitsky, Gennady; Shen, Yi
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.
ARO grant W911NF-07-1-0078, NSF grant DMS-1005903 and NSA grant H98230-11-1-0154
stationary process; global supremum location; bounded variation; strong mixing