An introduction to white–noise theory and Malliavin calculus for fractional Brownian motion
- 8 January 2004
- journal article
- research article
- Published by The Royal Society in Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
- Vol. 460 (2041), 347-372
- https://doi.org/10.1098/rspa.2003.1246
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.Keywords
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