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Dynamical systems on measure spaces, invariant measures, ergodic averages, mixing properties.
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Ergodicity of the product Markov chain
$\def\P{\mathsf{P}}$
Let $(X_n)_{n\in\mathbb{Z}_+}$ be a Markov chain with a transition kernel $P(x,dy)$. Consider now a product Markov chain $(X^1_n,X^2_n)_{n\in\mathbb{Z}_+}$ with the transition k …