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.
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页码：347 / 372
页数：26
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