稳定随机游走的凸包

IF 1.1 3区数学 Q2 STATISTICS & PROBABILITY

Electronic Journal of Probability Pub Date : 2022-01-01 DOI:10.1214/22-ejp826

W. Cygan, Nikola Sandri'c, Stjepan vSebek

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引用次数: 1

摘要

我们考虑随机漫步的凸壳，其步长属于一个稳定律的吸引域。我们证明了凸壳在具有Hausdorff距离的所有rd的凸和紧子集的空间中，向由极限稳定lsamvy过程的路径张成的凸壳收敛。作为一个应用，我们在随机漫步的一些温和的矩/结构假设下建立了(期望的)内在体积的收敛性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Convex hulls of stable random walks

We consider convex hulls of random walks whose steps belong to the domain of attraction of a stable law in Rd . We prove convergence of the convex hull in the space of all convex and compact subsets ofRd , 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.

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来源期刊

Electronic Journal of Probability 数学-统计学与概率论

CiteScore

1.80

自引率

7.10%

发文量

119

审稿时长

4-8 weeks

期刊介绍： The Electronic Journal of Probability publishes full-size research articles in probability theory. The Electronic Communications in Probability (ECP), a sister journal of EJP, publishes short notes and research announcements in probability theory. Both ECP and EJP are official journals of the Institute of Mathematical Statistics and the Bernoulli society.