In this continuation of the preceding paper (Part I), we consider a sequence ${\left(Fₙ\right)}_{n\ge 0}$ of i.i.d. random Lipschitz mappings → , where is a proper metric space. We investigate existence and uniqueness of invariant measures, as well as recurrence and ergodicity of the induced stochastic dynamical system (SDS) $X{ₙ}^x=Fₙ\circ ...\circ F₁\left(x\right)$ starting at x ∈ . The main results concern the case when the associated Lipschitz constants are log-centered. Principal tools are local contractivity, as considered in detail in Part I, the Chacon-Ornstein...

Consider a proper metric space and a sequence ${\left(Fₙ\right)}_{n\ge 0}$ of i.i.d. random continuous mappings → . It induces the stochastic dynamical system (SDS) $X{ₙ}^x=Fₙ\circ ...\circ F₁\left(x\right)$ starting at x ∈ . In this and the subsequent paper, we study existence and uniqueness of invariant measures, as well as recurrence and ergodicity of this process. In the present first part, we elaborate, improve and complete the unpublished work of Martin Benda on local contractivity, which merits publicity and provides an important tool for studying stochastic...