On the relationship between fractal dimension and fractal index for stationary stochastic processes

Hall, Peter ; Roy, Rahul (1994) On the relationship between fractal dimension and fractal index for stationary stochastic processes The Annals of Applied Probability, 4 (1). pp. 241-253. ISSN 1050-5164

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Official URL: http://projecteuclid.org/euclid.aoap/1177005210

Related URL: http://dx.doi.org/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.

Item Type:Article
Source:Copyright of this article belongs to Institute of Mathematical Statistics.
Keywords:Covariance; Fractal Dimension; Fractal Index; Fractional Index; Gaussian Process; Hausdorff Dimension; Level Crossing; Variogram
ID Code:72331
Deposited On:29 Nov 2011 11:23
Last Modified:29 Nov 2011 11:23

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