Limit theorems for supremum of Gaussian processes over a random interval  

作　　者：LIN Fu-ming PENG Zuo-xiang 

机构地区：[1]School of Statistics and Management, Shanghai University of Finance and Economics [2]School of Mathematics and Statistics, Sichuan University of Science & Engineering [3]School of Mathematics and Statistics, Southwestern University

出　　处：《Applied Mathematics(A Journal of Chinese Universities)》2018年第3期335-343,共9页高校应用数学学报（英文版）（B辑）

基　　金：Supported by the Scientific Research Fund of Sichuan Provincial Education Department(12ZB082);the Scientific research cultivation project of Sichuan University of Science&Engineering(2013PY07);the Scientific Research Fund of Shanghai University of Finance and Economics(2017110080);the Opening Project of Sichuan Province University Key Laboratory of Bridge Non-destruction Detecting and Engineering Computing(2018QZJ01)

摘　　要：Let {X(t), t ≥ 0} be a centered stationary Gaussian process with correlation r(t)such that 1-r(t) is asymptotic to a regularly varying function. With T being a nonnegative random variable and independent of X(t), the exact asymptotics of P(sup_(t∈[0,T])X(t) > x) is considered, as x → ∞.Let {X(t), t ≥ 0} be a centered stationary Gaussian process with correlation r(t)such that 1-r(t) is asymptotic to a regularly varying function. With T being a nonnegative random variable and independent of X(t), the exact asymptotics of P(sup_(t∈[0,T])X(t) > x) is considered, as x → ∞.

关 键 词：stationary Gaussian process supremum of a process regularly varying functions random intervals 

分 类 号：O1[理学—数学]