Distance from fractional Brownian motion with associated Hurst index to the subspaces of Gaussian martingales involving power integrands with an arbitrary positive exponent
Open Access
- 23 June 2020
- journal article
- research article
- Published by VTeX in Modern Stochastics: Theory and Applications
- Vol. 7 (2), 191-202
- https://doi.org/10.15559/20-vmsta156
Abstract
Publisher: VTeX - Solutions for Science Publishing, Journal: Modern Stochastics - Theory and Applications, Title: Distance from fractional Brownian motion with associated Hurst index 0, Authors: Oksana Banna, Filipp Buryak, Yuliya Mishura , We find the best approximation of the fractional Brownian motion with the Hurst index $H\in (0,1/2)$ by Gaussian martingales of the form ${\textstyle\int _{0}^{t}}{s^{\gamma }}d{W_{s}}$, where W is a Wiener process, $\gamma >0$.
Keywords
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