A remark on the mean square distance between the solutions of fractional SDEs and Brownian SDEs

Author: Saussereau Bruno  

Publisher: Taylor & Francis Ltd

ISSN: 1744-2508

Source: Stochastics: An International Journal of Probability and Stochastic Processes, Vol.84, Iss.1, 2012-02, pp. : 1-19

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Abstract

We study the family of solutions of differential equations driven by fractional Brownian motions when the Hurst parameter varies between 1/2 and 1. The drift and the diffusion coefficient may also vary in a family of differentiable functions. We prove that there exists a finite covering of this set of solutions by open balls of centred in some solutions of classical stochastic differential equations driven by a Brownian motion.