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Journal Articles Advances in Applied Probability Year : 2024

Topological reconstruction of compact supports of dependent stationary random variables

Sana Louhichi

Abstract

In this paper we extend results on reconstruction of probabilistic supports of random i.i.d variables to supports of dependent stationary $R^d$-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.
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Dates and versions

hal-04366871 , version 1 (30-12-2023)

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Public Domain

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Sadok Kallel, Sana Louhichi. Topological reconstruction of compact supports of dependent stationary random variables. Advances in Applied Probability, 2024, 56 (4), ⟨10.1017/apr.2024.4⟩. ⟨hal-04366871⟩
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