Baccelli, François; Hong, Dohy Analyticity of iterates of random non-expansive maps. (English) Zbl 0987.37047 Adv. Appl. Probab. 32, No. 1, 193-220 (2000). The authors show that the approach of Ruelle and Peres can be extended to address analyticity questions for iterates of certain classes of random non-expansive maps. 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. The authors also consider the case of reducible non-expansive operators, which arise in the modelling of open queueing networks, and for which differentiability and analyticity with respect to the parameters of the law are often open questions. Reviewer: Messoud Efendiev (Berlin) Cited in 2 Documents MSC: 37H99 Random dynamical systems 60H25 Random operators and equations (aspects of stochastic analysis) 47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc. 32D05 Domains of holomorphy 60B99 Probability theory on algebraic and topological structures 26E05 Real-analytic functions 47H40 Random nonlinear operators 34D08 Characteristic and Lyapunov exponents of ordinary differential equations 28A99 Classical measure theory Keywords:random non-expansive map; projective semi-norm PDFBibTeX XMLCite \textit{F. Baccelli} and \textit{D. Hong}, Adv. Appl. Probab. 32, No. 1, 193--220 (2000; Zbl 0987.37047) Full Text: DOI Link