Alternative forms of fractional Brownian motion

Alternative Frequency and Time Domain Versions of Fractional Brownian Motion

This paper compares models of fractional processes and associated weak convergence results based on moving average representations in the time domain with spectral representations. Both approaches have been applied in the literature on fractional processes. We point out that the conventional forms of these models are not equivalent, as is commonly assumed, even under a Gaussianity assumption. W...

Lacunary Fractional Brownian Motion

In this paper, a new class of Gaussian field is introduced called Lacunary Fractional Brownian Motion. Surprisingly we show that usually their tangent fields are not unique at every point. We also investigate the smoothness of the sample paths of Lacunary Fractional Brownian Motion using wavelet analysis.

Tempered fractional Brownian motion

Simulation of fractional Brownian motion

Preface In recent years, there has been great interest in the simulation of long-range dependent processes, in particular fractional Brownian motion. Motivated by applications in communications engineering, I wrote my master's thesis on the subject in 2002. Since many people turned out to be interested in various aspects of fractional Brownian motion, I decided to update my thesis and make it p...

Fractional Brownian motion and data

We analyze the fractal behavior of the high frequency part of the Fourier spectrum of fBm using multifractal analysis and show that it is not consistent with what is measured on real traac traces. We propose two extensions of fBm which come closer to actual traac traces multifractal properties.