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A stochastic contraction principle

We provide conditions for the existence of measurable solutions to the equation ξ(Tω) = f(ω, ξ(ω)), where T : Ω → Ω is an automorphism of the probability space Ω and f(ω, ·) is a strictly (but not necessarily uniformly) contracting mapping.

Keywords: Random dynamical systems, stochastic equations, contraction mappings, Perron- Frobenius theory

07/2007 | Random Operators and Stochastic Equations, Walter de Gruyter