Distance from fractional Brownian motion with associated Hurst index <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo mathvariant="normal"><</mo><mi mathvariant="italic">H</mi><mo mathvariant="normal"><</mo><mn>1</mn><mo mathvariant="normal" stretchy="false">/</mo><mn>2</mn></math> 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 ${\textstyle\int _{0}^{t}}{s^{\gamma }}d{W_{s}}$, where W is a Wiener process, $\gamma >0$.
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
VTeX
2020-06-01
|
| Series: | Modern Stochastics: Theory and Applications |
| Subjects: | |
| Online Access: | https://www.vmsta.org/doi/10.15559/20-VMSTA156 |