Theory of Probability and Mathematical Statistics
Approximation of a Wiener process by integrals with respect to the fractional Brownian motion of power functions of a given exponent
O. L. Banna, Yu. S. Mishura, S. V. Shklyar
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Abstract: The best uniform approximation of a Wiener process by integrals of the form ∫_{0}^{t}f(s)dB_{s}^{H} is established in the space L∞([0,T];L_2(Ω)), where {B_{t}^{H}, t\in[0,T]} is the fractional Brownian motion with the Hurst index H and f(s)=k•s^{α}, s\in[0,T], for k>0 and $ α=H-1/2.
Keywords: Wiener process, fractional Brownian motion, integral with respect to the fractional Brownian motion, an approximation in a class of functions
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