ABSTRAC Consider a proper metric space X and a sequence (Fn) of i.i.d. random continuous mappings from X to X. It induces the stochastic dynamical system (SDS) Xn = Fn ∘ ∘ ∘ F1(x) starting at x ∈ X. We study existence and uniqueness of invariant measures, under some assumptions of contraction on the Fn, as well as recurrence and ergodicity of this process. We will consider two main examples: the case where the Fn are affine maps of the real line and the case where Xn is the reflected random walk on the positive real line.