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

Oksana Banna; Filipp Buryak; Yuliya Mishura

doi:10.15559/20-vmsta156

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arXiv · 2006.14821

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

Oksana Banna·Filipp Buryak·Yuliya Mishura

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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 $\int _0^ts^{\gamma}dW_s$, where $W$ is a Wiener process, $\gamma >0$.

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Oksana Banna, Filipp Buryak, Yuliya Mishura. 2020-06-26. 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. https://doi.org/10.15559/20-vmsta156

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