Extending self-similarity for fractional Brownian motion

Author

Kaplan, Lance M. ; Kuo, C.-C Jay

Author_Institution

Dept. of Electr. Eng.-Syst., Univ. of Southern California, Los Angeles, CA, USA

Volume

42

Issue

12

fYear

1994

fDate

12/1/1994 12:00:00 AM

Firstpage

3526

Lastpage

3530

Abstract

The fractional Brownian motion (fBm) model has proven to be valuable in modeling many natural processes because of its persistence for large time lags. However, the model is characterized by one single parameter that cannot distinguish between short- and long-term correlation effects. This article investigates the idea of extending self-similarity to create a correlation model that generalizes discrete fBm referred to as asymptotic fBm (afBm). Namely, afBm is parameterized by variables controlling short- and long-term correlation effects. It proposes a fast parameter estimation algorithm for afBm based on the Haar transform, and demonstrates the performance of this parameter estimation algorithm with numerical simulations

Keywords

Brownian motion; correlation theory; parameter estimation; transforms; Haar transform; asymptotic fractional Brownian motion; correlation model; discrete fractional Brownian motion; extended self-similarity; fast parameter estimation algorithm; fractional Brownian motion; large time lags; long-term correlation effects; natural processes; numerical simulations; performance; short-term correlation effects; Brownian motion; Electric variables control; Electronic switching systems; Filters; Fractals; Gaussian noise; Parameter estimation; Signal processing; Signal processing algorithms; Wavelet transforms;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/78.340789

Filename

340789