Theory of Probability and Mathematical Statistics
Maximal coupling and V-stability of discrete nonhomogeneous Markov chains
V. V. Golomozyĭ, M. V. Kartashov
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Abstract: Two time-nonhomogeneous discrete Markov chains whose one-step transition probabilities are close in the V-variation norm are considered. The problem of stability of the expectation of f(X_n) with |f|≤V is studied for Markov chains. The main assumption imposed on a Markov chain is the V-mixing. The proofs are based on the maximal coupling procedure that maximize the one-step coupling probabilities.
Keywords: Coupling theory, coupling method, maximal coupling, discrete Markov chains, stability of distributions, test functions
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