A Regularization Approach to Fractional Dimension Estimation

François Roueff (1, 2) , Jacques Lévy Véhel (1)

1 FRACTALES - Fractals, complex models and artificial evolution
2 LTCI - Laboratoire Traitement et Communication de l'Information

We propose a new way of evaluating the regularity of a graph of a function f. Our approach is based on measuring the growth rate of the lengths of less and less regularized versions of f. This leads to a new index, that we call regularization dimension, dim_R . We derive some analytical properties of dim_R and compare it with other fractional dimensions. A statistical estimator is derived, and numerical experiments are performed, which suggest that dim_R may be computed in a robust way. Finally, we apply the regularization dimension to the study of Ethernet traffic.

Mots clés: Fractal dimension; regularization; estimation; multifractals; wavelets

Domaines: Probabilités [math.PR]

François Roueff, Jacques Lévy Véhel. A Regularization Approach to Fractional Dimension Estimation. Fractals 98, Oct 1998, Valleta, Malta. ⟨inria-00593254⟩