BOUNDS ON THE SUPREMA OF GAUSSIAN PROCESSES, AND OMEGA RESULTS FOR THE SUM OF A RANDOM MULTIPLICATIVE FUNCTION
成果类型：
Article
署名作者：
Harper, Adam J.
署名单位：
University of Cambridge
刊物名称：
ANNALS OF APPLIED PROBABILITY
ISSN/ISSBN：
1050-5164
DOI：
10.1214/12-AAP847
发表日期：
2013
页码：
584-616
关键词：
摘要：
We prove new lower bounds for the upper tail probabilities of suprema of Gaussian processes. Unlike many existing bounds, our results are not asymptotic, but supply strong information when one is only a little into the upper tail. We present an extended application to a Gaussian version of a random process studied by Halasz. This leads to much improved lower bound results for the sum of a random multiplicative function. We further illustrate our methods by improving lower bounds for some classical constants from extreme value theory, the Pickands constants H-alpha, as alpha -> 0.
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