IS THE LOCATION OF THE SUPREMUM OF A STATIONARY PROCESS NEARLY UNIFORMLY DISTRIBUTED?
成果类型：
Article
署名作者：
Samorodnitsky, Gennady; Shen, Yi
署名单位：
Cornell University
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
DOI：
10.1214/12-AOP787
发表日期：
2013
页码：
3494-3517
关键词：
摘要：
It is, perhaps, surprising that the location of the unique supremum of a stationary process on an interval can fail to be uniformly distributed over that interval. We show that this distribution is absolutely continuous in the interior of the interval and describe very specific conditions the density has to satisfy. We establish universal upper bounds on the density and demonstrate their optimality.