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Stochastic analysis, rough path analysis and fractional Brownian motions
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  • Published: January 2002

Stochastic analysis, rough path analysis and fractional Brownian motions

  • Laure Coutin1 &
  • Zhongmin Qian1 

Probability Theory and Related Fields volume 122, pages 108–140 (2002)Cite this article

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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.

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Authors and Affiliations

  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.fr, , , , , , FR

    Laure Coutin & Zhongmin Qian

Authors
  1. Laure Coutin
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  2. Zhongmin Qian
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Additional information

Received: 11 May 2000 / Revised version: 20 March 2001 / Published online: 11 December 2001

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Coutin, L., Qian, Z. Stochastic analysis, rough path analysis and fractional Brownian motions. Probab Theory Relat Fields 122, 108–140 (2002). https://doi.org/10.1007/s004400100158

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  • Issue Date: January 2002

  • DOI: https://doi.org/10.1007/s004400100158

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Keywords

  • Covariance
  • Limit Theorem
  • Integral Representation
  • Covariance Function
  • Gaussian Process
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