Packing dimensions of the images of Gaussian random fields

被引：2

作者：

Du, Yali ^{[1
]}

Miao, Junjie ^{[2
]}

Wu, Dongsheng ^{[3
]}

Xiao, Yimin ^{[4
]}

机构：

[1] S China Univ Technol, Sch Math, Guangzhou 510641, Guangdong, Peoples R China

[2] E China Normal Univ, Dept Math, Shanghai 200241, Peoples R China

[3] Univ Alabama, Dept Math Sci, Huntsville, AL 35899 USA

[4] Michigan State Univ, Dept Stat & Probabil, E Lansing, MI 48824 USA

来源：

STATISTICS & PROBABILITY LETTERS | 2015年 / 106卷

关键词：

Gaussian random fields; Packing dimension; Packing dimension profiles; Image sets; FRACTIONAL BROWNIAN-MOTION; RANDOM FRACTALS; PROFILES; PROJECTIONS; BOX;

D O I：

10.1016/j.spl.2015.07.020

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：

Let X = {X(t) : t is an element of R-N} be a Gaussian random field with values in R-d and let E subset of R-N be a Borel set. We determine the packing dimension of the image set X(E) in terms of the packing dimension profiles in the canonical metric rho of X, which are extensions of the packing dimension profiles of Falconer and Howroyd (1997) and the box-counting dimension profiles of Howroyd (2001). (C) 2015 Elsevier B.V. All rights reserved.

引用

页码：209 / 217

页数：9

共 50 条

[21] Redundancy in Gaussian random fields
De Bortoli, Valentin
Desolneux, Agnes
Galerne, Bruno
Leclaire, Arthur
ESAIM-PROBABILITY AND STATISTICS, 2020, 24 : 627 - 660
[22] THEOREM ON GAUSSIAN RANDOM FIELDS
DEO, CM
TEORIYA VEROYATNOSTEI I YEYE PRIMENIYA, 1973, 18 (02): : 384 - 387
[23] STRUCTURES IN RANDOM-FIELDS - GAUSSIAN FIELDS
BETANCORTRIJO, J
PHYSICAL REVIEW A, 1992, 45 (06): : 3447 - 3466
[24] RANDOM PACKING IN 2 DIMENSIONS AND STRUCTURE OF MONOLAYERS
QUICKENDEN, TI
TAN, GK
JOURNAL OF COLLOID AND INTERFACE SCIENCE, 1974, 48 (03) : 382 - 393
[25] PACKING DIMENSIONS OF GENERALIZED RANDOM MORAN SETS
Tong, Xin
Yu, Yue-Li
Zhao, Xiao-Jun
JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY, 2014, 51 (05) : 1075 - 1088
[26] RANDOM SEQUENTIAL PACKING IN 2 AND 3 DIMENSIONS
AKEDA, Y
HORI, M
BIOMETRIKA, 1976, 63 (02) : 361 - 366
[27] A labeling scheme based on Markov Random Fields and Gaussian mixture models for hyperspectral images
Huang, Xiu-Qin
Liao, Zhi-Wu
PROCEEDINGS OF 2008 INTERNATIONAL CONFERENCE ON MACHINE LEARNING AND CYBERNETICS, VOLS 1-7, 2008, : 3619 - +
[28] ASYMPTOTIC PROPERTIES OF GAUSSIAN RANDOM FIELDS
QUALLS, C
WATANABE, H
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1973, 177 (MAR) : 155 - 171
[29] Unified representation of Gaussian random fields
Poirion, F
Puig, B
ADVANCES IN STOCHASTIC STRUCTURAL DYNAMICS, 2003, : 393 - 400
[30] Gaussian Limits for Multidimensional Random Sequential Packing at Saturation
T. Schreiber
Mathew D. Penrose
J. E. Yukich
Communications in Mathematical Physics, 2007, 272 : 167 - 183

← 1 2 3 4 5 →