The Annals of Applied Probability
- Ann. Appl. Probab.
- Volume 4, Number 1 (1994), 241-253.
On the Relationship Between Fractal Dimension and Fractal Index for Stationary Stochastic Processes
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.
Ann. Appl. Probab., Volume 4, Number 1 (1994), 241-253.
First available in Project Euclid: 19 April 2007
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Hall, Peter; Roy, Rahul. On the Relationship Between Fractal Dimension and Fractal Index for Stationary Stochastic Processes. Ann. Appl. Probab. 4 (1994), no. 1, 241--253. doi:10.1214/aoap/1177005210. https://projecteuclid.org/euclid.aoap/1177005210