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

Biagini, Francesca ; Øksendal, Bernt; Sulem, Agnès and 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, Vol. 460, No. 2041: pp. 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.

• Item Type: Journal article
• Faculties: Mathematics, Computer Science and Statistics > Mathematics > Workgroup Financial Mathematics
• Subjects: 500 Science > 510 Mathematics
• ISSN: 1364-5021
• Language: English