Random iteration with place dependent probabilities

2011/07/04 by Rafał Kapica, Kapica, R., Maciej Ślęczka +1
Mathematics · #37A25 #60J05 #Dynamical Systems (math.DS) #FOS: Mathematics #Functional Equations Stability Results #Mathematical Dynamics and Fractals #Probability (math.PR) #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1107.0707

openalex publication_date 2011/07/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Markov chains arising from random iteration of functions S_θ:X→ X, θ∈ Θ, where X is a Polish space and Θ is arbitrary set of indices are considerd. At x∈ X, θ is sampled from distribution θ_x on Θ and θ_x are different for different x. Exponential convergence to a unique invariant measure is proved. This result is applied to case of random affine transformations on \mathbb R^d giving existence of exponentially attractive perpetuities with place dependent probabilities.

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