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
收藏
页码：347 / 372
页数：26
相关论文
共 50 条
  • [41] Application of the stochastic calculus of variation to the fractional Brownian motion
    Decreusefond, L
    Ustunel, AS
    COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 1995, 321 (12): : 1605 - 1608
  • [42] BISMUT-ELWORTHY-LI FORMULA, SINGULAR SDES, FRACTIONAL BROWNIAN MOTION, MALLIAVIN CALCULUS, STOCHASTIC FLOWS, STOCHASTIC VOLATILITY
    Amine, Oussama
    Coffie, Emmanuel
    Harang, Fabian
    Proske, Frank
    COMMUNICATIONS IN MATHEMATICAL SCIENCES, 2020, 18 (07) : 1863 - 1890
  • [43] Incorporating memory effect into a fractional stochastic diffusion particle tracking model for suspended sediment using Malliavin-Calculus-based fractional Brownian Motion
    Shen, Stanley W.
    Tsai, Christina W.
    CHAOS SOLITONS & FRACTALS, 2024, 187
  • [44] Applicability of White-Noise Techniques to Analyzing Motion Responses
    van Kleef, Joshua P.
    Stange, Gert
    Ibbotson, Michael R.
    JOURNAL OF NEUROPHYSIOLOGY, 2010, 103 (05) : 2642 - 2651
  • [45] Nonlinear filtering with fractional Brownian motion noise
    Zhao, X
    Zhao, XQ
    STOCHASTIC ANALYSIS AND APPLICATIONS, 2005, 23 (01) : 55 - 67
  • [46] Fractional white noise calculus and applications to finance
    Hu, YZ
    Oksendal, B
    INFINITE DIMENSIONAL ANALYSIS QUANTUM PROBABILITY AND RELATED TOPICS, 2003, 6 (01) : 1 - 32
  • [47] Fractional white noise calculus in infinite dimensions
    Grecksch, Wilfried
    Roth, Christian
    RANDOM OPERATORS AND STOCHASTIC EQUATIONS, 2014, 22 (03) : 179 - 193
  • [48] Path integrals for fractional Brownian motion and fractional Gaussian noise
    Meerson, Baruch
    Benichou, Olivier
    Oshanin, Gleb
    PHYSICAL REVIEW E, 2022, 106 (06)
  • [49] Permutation entropy of fractional Brownian motion and fractional Gaussian noise
    Zunino, L.
    Perez, D. G.
    Martin, M. T.
    Garavaglia, M.
    Plastino, A.
    Rosso, O. A.
    PHYSICS LETTERS A, 2008, 372 (27-28) : 4768 - 4774
  • [50] Bubble Entropy of Fractional Gaussian Noise and Fractional Brownian Motion
    Manis, George
    Bodini, Matteo
    Rivolta, Massimo W.
    Sassi, Roberto
    2021 COMPUTING IN CARDIOLOGY (CINC), 2021,
12345