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Analyticity of iterates of random non-expansive maps. (English) Zbl 0987.37047

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.

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
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