Fractional Brownian motion and long-range dependence. (English) Zbl 1039.60041

Doukhan, Paul (ed.) et al., Theory and applications of long-range dependence. Boston, MA: Birkhäuser (ISBN 0-8176-4168-8/hbk). 5-38 (2003).
The present paper is a well written tutorial about fractional Brownian motion (fBm) and some of its applications. The goal is to provide a basic introduction to the subject to allow the reader to tackle more specialized contributions involving limit theorems, statistical estimation and applications to modeling. Among others the following main topics are treated: Self-similarity, increment process of fBm and long-range dependence, FARIMA models, stochastic integral representation of Gaussian processes (in particular of fBm), application to time series, wavelet expansions of fBm.
For the entire collection see [Zbl 1005.00017].


60G15 Gaussian processes
60G18 Self-similar stochastic processes
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)