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Approximation of Fractional Brownian Motion by Martingales |
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| Authors: | Sergiy Shklyar Georgiy Shevchenko Yuliya Mishura Vadym Doroshenko Oksana Banna |
| Affiliation: | 1. Faculty of Mechanics and Mathematics, Kyiv National Taras Shevchenko University, Volodymyrska 64, 01601, Kyiv, Ukraine 2. Economics Faculty, Kyiv National Taras Shevchenko University, Volodymyrska 64, 01601, Kyiv, Ukraine |
| Abstract: | We study the problem of optimal approximation of a fractional Brownian motion by martingales. We prove that there exists 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. |
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