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

被引：72

作者：

Biagini, F

Oksendal, B

Sulem, A

Wallner, N

机构：

[1] Univ Bologna, Dept Math, I-40127 Bologna, Italy

[2] Univ Oslo, Dept Math, N-0316 Oslo, Norway

[3] Norwegian Sch Econ & Business Adm, N-5045 Bergen, Norway

[4] Inst Natl Rech Informat & Automat, F-78153 Le Chesnay, France

[5] Univ Oxford, Dept Math, Oxford OX1 3LB, England

来源：

PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES | 2004年 / 460卷 / 2041期

关键词：

fractional Brownian motion; white-noise theory; Malliavin calculus; Ito formula; Malliavin differentation;

D O I：

10.1098/rspa.2003.1246

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

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.

引用

页码：347 / 372

页数：26

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