Large Deviations for Markov Chains

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Large Deviations for Markov Chains is written by Alejandro D. de Acosta and published by . It's available with International Standard Book Number or ISBN identification 1009063359 (ISBN 10) and 9781009063357 (ISBN 13).

This book studies the large deviations for empirical measures and vector-valued additive functionals of Markov chains with general state space. Under suitable recurrence conditions, the ergodic theorem for additive functionals of a Markov chain asserts the almost sure convergence of the averages of a real or vector-valued function of the chain to the mean of the function with respect to the invariant distribution. In the case of empirical measures, the ergodic theorem states the almost sure convergence in a suitable sense to the invariant distribution. The large deviation theorems provide precise asymptotic estimates at logarithmic level of the probabilities of deviating from the preponderant behavior asserted by the ergodic theorems.