The Annals of Applied Probability

On the Relationship Between Fractal Dimension and Fractal Index for Stationary Stochastic Processes

Peter Hall and Rahul Roy

Full-text: Open access

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.

Article information

Source
Ann. Appl. Probab. Volume 4, Number 1 (1994), 241-253.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
http://projecteuclid.org/euclid.aoap/1177005210

JSTOR
links.jstor.org

Digital Object Identifier
doi:10.1214/aoap/1177005210

Mathematical Reviews number (MathSciNet)
MR1258183

Zentralblatt MATH identifier
0798.60035

Subjects
Primary: 60G10: Stationary processes
Secondary: 60G15: Gaussian processes 62G05: Estimation

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

Citation

Hall, Peter; Roy, Rahul. On the Relationship Between Fractal Dimension and Fractal Index for Stationary Stochastic Processes. The Annals of Applied Probability 4 (1994), no. 1, 241--253. doi:10.1214/aoap/1177005210. http://projecteuclid.org/euclid.aoap/1177005210.


Export citation