Fractional Brownian motion: theory and applications

Free access article

Issue		ESAIM: Proc. Volume 5, 1998 Fractional Differential Systems: Models, Methods and Applications


Page(s)		75 - 86
DOI		http://dx.doi.org/10.1051/proc:1998014

ESAIM: Proc., 1998, Vol. 5, pp. 75-86
DOI: 10.1051/proc:1998014

Fractional Brownian motion: theory and applications

Laurent Decreusefond and Ali Suleyman Üstünel

École Nationale Supérieure des Télécommunications, Département Informatique et Réseaux 46, rue Barrault, 75 634 Paris Cedex 13, France

Abstract
We present new theoretical results on the fractional Brownian motion, including different definitions (and their relationships) of the stochastic integral with respect to this process, Girsanov theorem, Clark representation formula, Itô formula and so on. Several applications (such as non-linear filtering theory, queuing networks, mathematical finance) are given as applied examples of these theoretical results.

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