The distance between fractional Brownian motion and the subspace of martingales with “similar” kernels
Анотація
We study the problem of approximation of a fractional Brownian motion with the help of Gaussian martingales that can be represented as the integrals with respect to a Wiener process and with nonrandom integrands being âsimilarâ to the kernel of the fractional Brownian motion. The âsimilarityâ is understood in the sense that an integrand is the value of the kernel at some point. We establish analytically and evaluate numerically the upper and lower bounds for the distance between the fractional Brownian motion and the space of Gaussian martingales.
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