Contractivity and Ergodicity of the Random Map X → |x − Θ| *
نویسنده
چکیده
The long time behavior of the random map xn → xn+1 = |xn − θn| is studied under various assumptions on the distribution of the θn. One of the interesting features of this random dynamical system is that for a single fixed deterministic θ the map is not a contraction, while the composition is almost surely a contraction if θ is chosen randomly with only mild assumptions on the distribution of the θ’s. The system is useful as an explicit model where more abstract ideas can be explored concretely. We explore various measures of convergence rates, hyperbolically from randomness, and the structure of the random attractor.
منابع مشابه
Stochastic Dynamical Systems with Weak Contractivity Properties I. Strong and Local Contractivity Marc Peigné and Wolfgang Woess with a Chapter Featuring Results of Martin Benda
Consider a proper metric space X and a sequence (Fn)n≥0 of i.i.d. random continuous mappings X → X. It induces the stochastic dynamical system (SDS) X n = Fn ◦ · · · ◦ F1(x) starting at x ∈ 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 comple...
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