THE RELATIONSHIP BETWEEN DIMENSION AND FRACTAL INDEX FOR STATIONARY STOCHASTIC PROCESSES

被引：34

作者：

Hall, Peter ^{[1
]}

Roy, Rahul

机构：

[1] Australian Natl Univ, CMA, Canberra, ACT 2601, Australia

来源：

ANNALS OF APPLIED PROBABILITY | 1994年 / 4卷 / 01期

关键词：

Covariance; fractal dimension; fractal index; fractional index; Gaussian process; Hausdorff dimension; level crossing; variogram;

D O I：

10.1214/aoap/1177005210

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：

For Gaussian processes there is a simple and well-known relationship between the fractal dimension of sample paths and the fractal index of the covariance function. This property is of considerable practical interest, since it forms the basis of several estimators of fractal dimension. Motivated by statistical applications involving non-Gaussian processes, we discuss the relationship in a wider context. We show that the relationship fails in some circumstances, but nevertheless does hold in a variety of cases.

引用

页码：241 / 253

页数：13

共 50 条

[21] THE RELATIONSHIP BETWEEN FRACTAL DIMENSION AND TERTIARY STRUCTURE OF PROTEIN MOLECULE
WANG, CX
SHI, YY
HUANG, FH
[J]. CHINESE SCIENCE BULLETIN, 1991, 36 (06): : 499 - 503
[22] Relationship between the fractal dimension and Krumbein's roundness number
Vallejo, L.E.
Zhou, Y.
[J]. Soils and Foundations, 1995, 35 (01):
[23] The study of the relationship between the condition of image acquisition and the fractal dimension
An, BM
Heo, MS
Lee, SP
Lee, SS
Choi, SC
Park, TW
[J]. JOURNAL OF DENTAL RESEARCH, 2002, 81 : B325 - B325
[24] Relationship between Compressive Strength and Fractal Dimension of Pore Structure
Wang Jianzhong
Tang Huiping
Zhu Jilei
Ao Qingbo
Zhi Hao
Ma Jun
[J]. RARE METAL MATERIALS AND ENGINEERING, 2013, 42 (12) : 2433 - 2436
[25] Methods of measuring the fractal dimension and fractal signatures of a multidimensional stochastic
Potapov, AA
German, VA
[J]. JOURNAL OF COMMUNICATIONS TECHNOLOGY AND ELECTRONICS, 2004, 49 (12) : 1370 - 1391
[26] Simulation of multivariate stationary stochastic processes using dimension-reduction representation methods
Liu, Zhangjun
Liu, Zenghui
Peng, Yongbo
[J]. JOURNAL OF SOUND AND VIBRATION, 2018, 418 : 144 - 162
[27] Stochastic models for fractal processes
Anh, VV
Heyde, CC
Tieng, Q
[J]. JOURNAL OF STATISTICAL PLANNING AND INFERENCE, 1999, 80 (1-2) : 123 - 135
[28] Records in fractal stochastic processes
Aliakbari, A.
Manshour, P.
Salehi, M. J.
[J]. CHAOS, 2017, 27 (03)
[29] FRACTAL DIMENSION FOR GAUSSIAN COLORED PROCESSES
LLOSA, J
MASOLIVER, J
[J]. PHYSICAL REVIEW A, 1990, 42 (08): : 5011 - 5014
[30] Relationship between the fractal dimension of orthopyroxene distribution and the temperature in mantle xenoliths
Nkono, Collin
Femenias, Olivier
Lesne, Annick
Mercier, Jean-Claude
Ngounouno, Fadimatou Yamgouot
Demaiffe, Daniel
[J]. GEOLOGICAL JOURNAL, 2016, 51 (05) : 748 - 759

← 1 2 3 4 5 →