Random iteration with place dependent probabilities

Abstract

Markov chains arising from random iteration of functions $S_{\theta }:X\to X$, $\theta \in \Theta$, where $X$ is a Polish space and $\Theta$ is arbitrary set of indices are considerd. At $x\in X$, $\theta$ is sampled from distribution ${\theta }_x$ on $\Theta$ and ${\theta }_x$ 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.

arXiv commentRevised version

Cited by in corpus (2)

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