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Probability Theory and Related Fields

, Volume 122, Issue 1, pp 108–140 | Cite as

Stochastic analysis, rough path analysis and fractional Brownian motions

  • Laure Coutin
  • Zhongmin Qian

Abstract.

 In this paper we show, by using dyadic approximations, the existence of a geometric rough path associated with a fractional Brownian motion with Hurst parameter greater than 1/4. Using the integral representation of fractional Brownian motions, we furthermore obtain a Skohorod integral representation of the geometric rough path we constructed. By the results in [Ly1], a stochastic integration theory may be established for fractional Brownian motions, and strong solutions and a Wong-Zakai type limit theorem for stochastic differential equations driven by fractional Brownian motions can be deduced accordingly. The method can actually be applied to a larger class of Gaussian processes with covariance functions satisfying a simple decay condition.

Keywords

Covariance Limit Theorem Integral Representation Covariance Function Gaussian Process 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Laure Coutin
    • 1
  • Zhongmin Qian
    • 1
  1. 1.CNRS and Université Paul-Sabatier, Laboratoire de Statistique et Probabilités, 118 Route de Narbonne, 31062 Toulouse, France. e-mail: coutin@cict.fr; qian@cict.frFR

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