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Topological reconstruction of compact supports of dependent stationary random variables

Published online by Cambridge University Press:  02 April 2024

Sadok Kallel*
American University of Sharjah
Sana Louhichi*
Université Grenoble Alpes
*Postal address: American University of Sharjah, UAE, and Laboratoire Painlevé, Université de Lille, France. Email address:
**Postal address: Université Grenoble Alpes, CNRS, Grenoble INP, LJK 38000 Grenoble, France. Email address:


In this paper we extend results on reconstruction of probabilistic supports of independent and identically distributed random 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.

Original Article
© The Author(s), 2024. Published by Cambridge University Press on behalf of Applied Probability Trust

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