EXTREMES OF A CLASS OF NONHOMOGENEOUS GAUSSIAN RANDOM FIELDS

• 成果类型: Article
• 署名作者: Debicki, Krzysztof; Hashorva, Enkelejd; Ji, Lanpeng
• 署名单位: University of Wroclaw
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/14-AOP994
• 发表日期: 2016
• 页码: 984-1012
• 关键词: fractional brownian-motion; stationary-processes; shepp statistics; probabilities; supremum; maximum; infimum

摘要

This contribution establishes exact tail asymptotics of sup((s,t)) is an element of E X(s,t) for a large class of nonhomogeneous Gaussian random fields X on a bounded convex set E subset of R-2, with variance function that attains its maximum on a segment on E. These findings extend the classical results for homogeneous Gaussian random fields and Gaussian random fields with unique maximum point of the variance. Applications of our result include the derivation of the exact tail asymptotics of the Shepp statistics for stationary Gaussian processes, Brownian bridge and fractional Brownian motion as well as the exact tail asymptotic expansion for the maximum loss and span of stationary Gaussian processes.