论文标题
分数布朗运动水平集的尺寸的统一结果
A uniform result for the dimension of fractional Brownian motion level sets
论文作者
论文摘要
令$ b = \ {b_t \，：\，t \ geq 0 \} $为索引$ h \ in（0,1）$的真实价值分数布朗运动。我们证明了级别的宏观Hausdorff尺寸设置$ \ MATHCAL {l} _x = \ left \ {t \ in \ Mathbb {r} _+ \，：\，：\，b_t = x \ x \ right \} $ ins，libaligity ins，与$ 1-$ x \ $ x \ in c \ ins for Phipobility One ins in c。
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 $x\in\mathbb{R}$.
