论文标题
稳定随机步行的凸面
Convex hulls of stable random walks
论文作者
论文摘要
我们考虑了随机步行的凸壳，其步骤属于$ \ Mathbb {r}^d $中稳定定律吸引的领域。我们证明了所有凸的空间中凸壳的融合，配备有Hausdorff距离的$ \ Mathbb {r}^d $的紧凑子集朝向凸出的凸壳，该凸壳由极限稳定的lévy流程的路径跨越。作为一种应用，我们在随机步行中提出的一些轻度力矩/结构假设下建立了（预期）内在体积的收敛性。
We consider convex hulls of random walks whose steps belong to the domain of attraction of a stable law in $\mathbb{R}^d$. We prove convergence of the convex hull in the space of all convex and compact subsets of $\mathbb{R}^d$, equipped with the Hausdorff distance, towards the convex hull spanned by a path of the limit stable Lévy process. As an application, we establish convergence of (expected) intrinsic volumes under some mild moment/structure assumptions posed on the random walk.
