A uniform result for the dimension of fractional Brownian motion level sets
| Autor: | Daw, Lara |
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| Rok vydání: | 2020 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1016/S0167-7152(96)00151-4 |
| Popis: | Let $B =\{ B_t \, : \, t \geq 0 \}$ be a real-valued fractional Brownian motion of index $H \in (0,1)$. We prove that the macroscopic Hausdorff dimension of the level sets $\mathcal{L}_x = \left\{ t \in \mathbb{R}_+ \, : \, B_t=x \right\}$ is, with probability one, equal to $1-H$ for all $x\in\mathbb{R}$. |
| Databáze: | arXiv |
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