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

Modern Stochastics: Theory and Applications

Oksana Banna¹  Yuliya Mishura²  Filipp Buryak² 

[1] Kyiv National Taras Shevchenko University, Faculty of Economics, Volodymyrska 64, 01601 Kyiv, Ukraine;Kyiv National Taras Shevchenko University, Faculty of Mechanics and Mathematics, Volodymyrska 64, 01601 Kyiv, Ukraine;

关键词: fractional Brownian motion;    Martingale;    approximation;   

DOI  :  10.15559/20-VMSTA156

来源: DOAJ

【 摘 要 】

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, $\gamma >0$.

【 授权许可】

Unknown