Distance from fractional Brownian motion with associated Hurst index to the subspaces of Gaussian martingales involving power integrands with an arbitrary positive exponent
Volume 7, Issue 2 (2020), pp. 191–202
Pub. online: 23 June 2020
Type: Research Article
Open Access
Open Access
Received
22 April 2020
22 April 2020
Revised
6 June 2020
6 June 2020
Accepted
6 June 2020
6 June 2020
Published
23 June 2020
23 June 2020
Abstract
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, $\gamma >0$.
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