S. M. Prigarin, K. Hahn, G. Winkler, “Comparative analysis of two numerical methods to measure Hausdorff dimension of the fractional Brownian motion”, Sib. Zh. Vychisl. Mat., 2008, Volume 11, Number 2,Pages <nobr>201

This article is cited in 17 papers

Comparative analysis of two numerical methods to measure Hausdorff dimension of the fractional Brownian motion

S. M. Prigarin^a, K. Hahn^b, G. Winkler^b

^a Institute of Computational Mathematics and Mathematical Geophysics (Computing Center), Siberian Branch of the Russian Academy of Sciences
^b Institute of Biomathematics and Biometry Helmholtz Zentrum München

Abstract: The objective of the paper is to study by Monte Carlo simulation statistical properties of two numerical methods (the extended counting method and the variance counting method) developed to estimate the Hausdorff dimension of a time series and applied to the fractional Brownian motion.

Key words: fractal set, Hausdorff dimension, extended counting method, variance counting method, generalized Wiener process, fractional Brownian motion.

MSC: 28A80, 62M10, 65C05

Received: 08.02.2007