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

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