Geodesic
Approximation of fractional brownian motion with associated hurst index separated from 1 by stochastic integrals of linear power functions
Teoriâ slučajnyh processov, Tome 14 (2008) no. 3, pp. 1-16

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In this article we present the best uniform approximation of the fractional Brownian motion in space $ L_\infty([0, T]; L_2 (\Omega))$ by martingales of the following type $\int^t_0a(s)dW_s,$ where $W$ is a Wiener process,$a$ is a function defined by $a(s)=k_1+k_2s^\alpha, k_1,k_2\in{\mathbb R}, s\in[0, T],$ $\alpha=H-1/2,$ $H$ is the Hurst index, separated from 1, associated with the fractional Brownian motion.
Keywords: Fractional Brownian motion, Wiener integral, approximation. 
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     author = {Oksana Banna and Yuliya Mishura},
     title = {Approximation of fractional brownian motion with associated hurst index separated from 1 by stochastic integrals of linear power functions},
     journal = {Teori\^a slu\v{c}ajnyh processov},
     pages = {1--16},
     publisher = {mathdoc},
     volume = {14},
     number = {3},
     year = {2008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/THSP_2008_14_3_a0/}
}
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Oksana Banna; Yuliya Mishura. Approximation of fractional brownian motion with associated hurst index separated from 1 by stochastic integrals of linear power functions. Teoriâ slučajnyh processov, Tome 14 (2008) no. 3, pp. 1-16. http://geodesic.mathdoc.fr/item/THSP_2008_14_3_a0/