On limit theorems for persistent Betti numbers from dependent data

Johannes Krebs

Stochastic Processes and their Applications, 2021, vol. 139, issue C, 139-174

Abstract: 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, βqr,s, 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 βqr,s in the critical regime under quite general dependence settings.

Keywords: Critical regime; Dependent data; Limit theorems; Markov chains; Marton coupling; Topological data analysis (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1016/j.spa.2021.04.013

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