Exact L2 small balls of Gaussian processes

被引：19

作者：

Gao, F

Hannig, J

Lee, TY

Torcaso, F ^{[1
]}

机构：

[1] Johns Hopkins Univ, Dept Appl Math & Stat, Baltimore, MD 21218 USA

[2] Univ Idaho, Dept Math, Moscow, ID 83844 USA

[3] Colorado State Univ, Dept Stat, Ft Collins, CO 80523 USA

[4] Univ Maryland, Dept Math, College Pk, MD 20742 USA

来源：

JOURNAL OF THEORETICAL PROBABILITY | 2004年 / 17卷 / 02期

基金：

美国国家科学基金会;

关键词：

small ball probabilities; integrated Brownian motions; comparison theorems;

D O I：

10.1023/B:JOTP.0000020705.28185.4c

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 prove a comparison theorem extending Li-(6) and develop a complex-analytic approach to treat L-2 small ball probabilities of Gaussian processes. We demonstrate the techniques for the m-times integrated Brownian motions and in examples where one can not apply Li comparison theorem.

引用

页码：503 / 520

页数：18

共 7 条

[1]

[Anonymous], 1974, REAL COMPLEX ANAL

[2] EXACT BEHAVIOR OF GAUSSIAN SEMINORMS [J].

DEMBO, A ;

MAYERWOLF, E ;

ZEITOUNI, O .

STATISTICS & PROBABILITY LETTERS, 1995, 23 (03) :275-280

[3]

GAO F, IN PRESS ANN PROBAB

[4]

Hadamard J., 1893, Bull. Sci. Math., V2, P240

[5] LOWER TAIL OF GAUSSIAN SEMINORMS [J].

HOFFMANNJORGENSEN, J ;

SHEPP, LA ;

DUDLEY, RM .

ANNALS OF PROBABILITY, 1979, 7 (02) :319-342

[6]

LI WV, 1992, J THEOR PROBAB, V5, P1

[7]

SYTAYA GN, 1974, THEORY STOCHASTIC PR, V2, P93

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