PROBABILITY TAILS OF GAUSSIAN EXTREMA

被引：28

作者：

SAMORODNITSKY, G

机构：

[1] Cornell University, Engineering and Theory Center, Ithaca, NY 14853-7501, Upson Hall

来源：

STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 1991年 / 38卷 / 01期

关键词：

GAUSSIAN PROCESSES; ISONORMAL PROCESS; SUPREMUM; METRIC ENTROPY; BROWNIAN SHEET; EMPIRICAL PROCESSES;

D O I：

10.1016/0304-4149(91)90072-K

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We study the supremum of 'the' standard isonormal linear process L on a subset C of a real Hilbert space H. Upper and lower bounds on the probability that sup(x-epsilon-C) Lx > lambda, lambda large, are found. We treat a number of examples. These include the distribution of the maximum of certain 'locally stationary' processes on R1, as well as those of the rectangle indexed, pinned Brownian sheet in R(k) and the half-plane indexed pinned sheet in R2. We also consider Brownian motion indexed by convex sets in [0, 1]2.

引用

页码：55 / 84

页数：30

共 20 条

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