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.

翻译：本文将对独立同分布随机变量概率支撑重构的结果推广至相依平稳$\mathbb R^d$值随机变量的支撑情形。假设所有支撑均为欧氏空间中具有正可达性质的紧集。主要结果涉及相依平稳随机向量云在Hausdorff意义下收敛至其公共支撑的研究。本文提出了新的拓扑重构结果，并给出了多个示例说明。最后以圆上的Möbius马尔可夫链为例进行数值模拟分析。