Stochastic analysis, rough path analysis and fractional Brownian motions View Full Text


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Article Info

DATE

2002-01

AUTHORS

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. More... »

PAGES

108-140

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s004400100158

DOI

http://dx.doi.org/10.1007/s004400100158

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1043723250


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