Topological reconstruction of compact supports of dependent stationary random variables

Sadok Kallel (1, 2) , Sana Louhichi (3)

1 Université de Lille
2 American University of Sharjah
3 IPS - Inférence Processus Stochastiques

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.

Keywords: Hausdorff distance; stationary dependent random variables; mixing Markov chain; compact support; concentration positive reach; topological inference

Domains: Mathematics [math]; Statistics [math.ST]

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