Topological reconstruction of compact supports of dependent stationary random variables

Fuente: arXiv
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Main Authors: Kallel, Sadok, Louhichi, Sana
Format: Preprint
Published: 2023
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author Kallel, Sadok
Louhichi, Sana
author_facet Kallel, Sadok
Louhichi, Sana
contents In this paper we extend results on reconstruction of probabilistic supports of random i.i.d variables to supports of dependent stationary $\mathbb R^d$-valued random variables. All supports are assumed to be compact of positive reach in Euclidean space. Our main results involve the study of the convergence in the Hausdorff sense of a cloud of stationary dependent random vectors to their common support. A novel topological reconstruction result is stated, and a number of illustrative examples are presented. The example of the Möbius Markov chain on the circle is treated at the end with simulations.
format Preprint
id arxiv_https___arxiv_org_abs_2307_11674
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Topological reconstruction of compact supports of dependent stationary random variables
Kallel, Sadok
Louhichi, Sana
Probability
Statistics Theory
In this paper we extend results on reconstruction of probabilistic supports of random i.i.d variables to supports of dependent stationary $\mathbb R^d$-valued random variables. All supports are assumed to be compact of positive reach in Euclidean space. Our main results involve the study of the convergence in the Hausdorff sense of a cloud of stationary dependent random vectors to their common support. A novel topological reconstruction result is stated, and a number of illustrative examples are presented. The example of the Möbius Markov chain on the circle is treated at the end with simulations.
title Topological reconstruction of compact supports of dependent stationary random variables
topic Probability
Statistics Theory
url https://arxiv.org/abs/2307.11674