  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
M\"{o}bius Markov chain on the circle is treated at the end with simulations.
