Distance from fractional Brownian motion with associated Hurst index $0<H<1/2$ to the subspaces of Gaussian martingales involving power integrands with an arbitrary positive exponent

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 ${\int }_0^t{s}^{\gamma }d{W}_s$, where $W$ is a Wiener process, $\gamma >0$.

Published at https://doi.org/10.15559/20-VMSTA156 in the Modern Stochastics: Theory and Applications (https://vmsta.org/) by VTeX (http://www.vtex.lt/)

References in corpus (1)

• Approximation of fractional Brownian motion by martingales