On limit theorems for persistent Betti numbers from dependent data

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:139

Article

Krebs, Johannes¹ 

[1] Heidelberg Univ, Inst Appl Math, Im Neuenheimer Feld 205, D-69120 Heidelberg, Germany

关键词: Critical regime;    Dependent data;    Limit theorems;    Markov chains;    Marton coupling;    Topological data analysis;   

DOI  :  10.1016/j.spa.2021.04.013

来源: Elsevier

【 摘 要 】

We study persistent Betti numbers and persistence diagrams obtained from time series and random fields. It is well known that the persistent Betti function is an efficient descriptor of the topology of a point cloud. So far, convergence results for the (r, s)-persistent Betti number of the qth homology group, beta(r,s)(q) , were mainly considered for finite-dimensional point cloud data obtained from i.i.d. observations or stationary point processes such as a Poisson process. In this article, we extend these considerations. We derive limit theorems for the pointwise convergence of persistent Betti numbers beta(q) (r,s) in the critical regime under quite general dependence settings. (C) 2021 Elsevier B.V. All rights reserved.

【 授权许可】

Free