An introduction to white–noise theory and Malliavin calculus for fractional Brownian motion

Biagini, Francesca ; Øksendal, Bernt; Sulem, Agnès und Wallner, Naomi (2004): An introduction to white–noise theory and Malliavin calculus for fractional Brownian motion. In: Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, Bd. 460, Nr. 2041: S. 347-372

Abstract

Fractional Brownian motion (FBM) with Hurst parameter index between 0 and 1 is a stochastic process originally introduced by Kolmogorov in a study of turbulence. Many other applications have subsequently been suggested. In order to obtain good mathematical models based on FBM, it is necessary to have a stochastic calculus for such processes. The purpose of this paper is to give an introduction to this newly developed theory of stochastic integration for FBM based on white-noise theory and (Malliavin–type) differentiation.

• Dokumententyp: Zeitschriftenartikel
• Fakultät: Mathematik, Informatik und Statistik > Mathematik > Finanz- und Versicherungsmathematik
• Themengebiete: 500 Naturwissenschaften und Mathematik > 510 Mathematik
• ISSN: 1364-5021
• Sprache: Englisch