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 50 条

[21] L2 limits of generalized Jirina processes
Lv, You
Li, Yuqiang
STATISTICS & PROBABILITY LETTERS, 2017, 129 : 288 - 296
[22] Local stationarity of L2 (R) processes
Garcia, FM
Lourtie, IMG
Buescu, J
2002 IEEE INTERNATIONAL CONFERENCE ON ACOUSTICS, SPEECH, AND SIGNAL PROCESSING, VOLS I-IV, PROCEEDINGS, 2002, : 1221 - 1224
[23] Logarithmic L2-small ball asymptotics for some fractional Gaussian processes
Nazarov, AI
Nikitin, YY
THEORY OF PROBABILITY AND ITS APPLICATIONS, 2004, 49 (04) : 645 - 658
[24] Sharp small deviation asymptotics in the L2-norm for a class of Gaussian processes
Nikitin Ya.Yu.
Kharinski P.A.
Journal of Mathematical Sciences, 2006, 133 (3) : 1328 - 1332
[25] EXACT BEHAVIOR OF GAUSSIAN MEASURES OF TRANSLATED BALLS IN HILBERT-SPACES
LINDE, W
ROSINSKI, J
JOURNAL OF MULTIVARIATE ANALYSIS, 1994, 50 (01) : 1 - 16
[26] Exact L2 Bernstein-Markov inequality on the ball
Kroo, Andras
JOURNAL OF APPROXIMATION THEORY, 2022, 281
[27] DIMENSION-FREE ESTIMATES ON l2(Zd) FOR A DISCRETE DYADIC MAXIMAL FUNCTION OVER l1 BALLS: SMALL SCALES
Niksinski, Jakub
COLLOQUIUM MATHEMATICUM, 2024, 175 (01) : 37 - 54
[28] Exact values of widths of certain classes of periodic differentiable functions in the space L2[0, 2π]Точные значение поперечников некоторых классов периодических дифференцируемых функциИ в пространстве L2 [0, 2п]
M. Sh. Shabozov
K. K. Palavonov
Analysis Mathematica, 2015, 41 : 103 - 115
[29] Online Learning in L2 Space with Multiple Gaussian Kernels
Ohnishi, Motoya
Yukawa, Masahiro
2017 25TH EUROPEAN SIGNAL PROCESSING CONFERENCE (EUSIPCO), 2017, : 1594 - 1598
[30] Asymptotic distribution of L2 affinity between Gaussian densities
Boumaza, R
COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 1999, 328 (06): : 527 - 529

← 1 2 3 4 5 →