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