Integral transformations and anticipative calculus for fractional Brownian motions
Author(s)
Bibliographic Information
Integral transformations and anticipative calculus for fractional Brownian motions
(Memoirs of the American Mathematical Society, no. 825)
American Mathematical Society, c2005
Available at 18 libraries
  Aomori
  Iwate
  Miyagi
  Akita
  Yamagata
  Fukushima
  Ibaraki
  Tochigi
  Gunma
  Saitama
  Chiba
  Tokyo
  Kanagawa
  Niigata
  Toyama
  Ishikawa
  Fukui
  Yamanashi
  Nagano
  Gifu
  Shizuoka
  Aichi
  Mie
  Shiga
  Kyoto
  Osaka
  Hyogo
  Nara
  Wakayama
  Tottori
  Shimane
  Okayama
  Hiroshima
  Yamaguchi
  Tokushima
  Kagawa
  Ehime
  Kochi
  Fukuoka
  Saga
  Nagasaki
  Kumamoto
  Oita
  Miyazaki
  Kagoshima
  Okinawa
  Korea
  China
  Thailand
  United Kingdom
  Germany
  Switzerland
  France
  Belgium
  Netherlands
  Sweden
  Norway
  United States of America
Note
"Volume 175, number 825 (first of 4 numbers)."
Includes bibliographical references (p. 123-127)
Description and Table of Contents
Description
This paper studies two types of integral transformation associated with fractional Brownian motion. They are applied to construct approximation schemes for fractional Brownian motion by polygonal approximation of standard Brownian motion. This approximation is the best in the sense that it minimizes the mean square error. The rate of convergence for this approximation is obtained. The integral transformations are combined with the idea of probability structure preserving mapping introduced in [48] and are applied to develop a stochastic calculus for fractional Brownian motions of all Hurst parameter $H\in (0, 1)$.In particular we obtain Radon-Nikodym derivative of nonlinear (random) translation of fractional Brownian motion over finite interval, extending the results of [48] to general case. We obtain an integration by parts formula for general stochastic integral and an Ito type formula for some stochastic integral. The conditioning, Clark derivative, continuity of stochastic integral are also studied. As an application we study a linear quadratic control problem, where the system is driven by fractional Brownian motion.
Table of Contents
Introduction Representations Induced transformation I Approximation Induced transformation II Stochastic calculus of variation Stochastic integration Nonlinear translation (Absolute continuity) Conditional expectation Integration by parts Composition (Ito formula) Clark type representation Continuation Stochastic control Appendix Bibliography.
by "Nielsen BookData"