arXiv subjects

Oksana Banna

Publications and source records attributed to Oksana Banna.

2 recordsLinked to original sources

arXiv2020

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

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 $\int _0^ts^γdW_s$, where $W$ is a Wiener process, $γ>0$.

math.PR↗

arXiv2012

Approximation of fractional Brownian motion by martingales

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.

math.PR↗