Sergiy Shklyar, Georgiy Shevchenko, Yuliya Mishura, Vadym Doroshenko, Oksana Banna
Published 2012-05-21Version 1
We study the problem of optimal approximation of a fractional Brownian motion by martingales. We prove that there exist a unique martingale closest to fractional Brownian motion in a specific sense. It shown that this martingale has a specific form. Numerical results concerning the approximation problem are given.
Fractional martingales and characterization of the fractional Brownian motion
Large deviations for local times and intersection local times of fractional Brownian motions and Riemann-Liouville processes
Joint convergence along different subsequences of the signed cubic variation of fractional Brownian motion
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