Analyticity of iterates of random non-expansive maps

This paper focuses on the analyticity of the limiting behavior of a class o f dynamical systems defined by iteration of non-expansive random operators. The analyticity is understood with respect to the parameters which govern the law of the operators. The proofs are based on contraction with respect to certain projective semi-norms. Several examples are considered, includin g Lyapunov exponents associated with products of random matrices both in th e conventional algebra, and in the (max, +) semi-field, and Lyapunov expone nts associated with non-linear dynamical systems arising in stochastic cont rol. For the class of reducible operators (defined in the paper), we also a ddress the issue of analyticity of the expectation of functionals of the li miting behavior, and connect this with contraction properties with respect to the supremum norm. We give several applications to queueing theory.