In this paper, we extend estimation results on the $R$-convex hull of the points of a random sample from independence to some dependent cases. Explicit convergence rates are obtained in that case; we deal with $R$-convex hulls and its natural plug-in to estimate the support $S$ or level-sets together with their volume and perimeter of the marginal density $f$ on $\R^d$, of a strictly stationary process. For this we assume some weak dependence conditions and different distributional assumption depending on the estimation purpose (support or level sets estimation). The loss with regard to the classical independent case depends on the current dependence structure.