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February, 1994 On the Relationship Between Fractal Dimension and Fractal Index for Stationary Stochastic Processes
Peter Hall, Rahul Roy
Ann. Appl. Probab. 4(1): 241-253 (February, 1994). DOI: 10.1214/aoap/1177005210

Abstract

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.

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Peter Hall. Rahul Roy. "On the Relationship Between Fractal Dimension and Fractal Index for Stationary Stochastic Processes." Ann. Appl. Probab. 4 (1) 241 - 253, February, 1994. https://doi.org/10.1214/aoap/1177005210

Information

Published: February, 1994
First available in Project Euclid: 19 April 2007

zbMATH: 0798.60035
MathSciNet: MR1258183
Digital Object Identifier: 10.1214/aoap/1177005210

Subjects:
Primary: 60G10
Secondary: 60G15 , 62G05

Keywords: Covariance , fractal dimension , fractal index , fractional index , Gaussian process , Hausdorff dimension , level crossing , variogram

Rights: Copyright © 1994 Institute of Mathematical Statistics

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Vol.4 • No. 1 • February, 1994
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