Identification of the rate function for large deviations of an irreducible Markov chain
Wei Liu, Wuhan University
Liming Wu, Université Blaise Pascal
Abstract
For an irreducible Markov chain $(X_n)_{nge 0}$ we identify the rate function
governing the large deviation estimation of empirical mean $frac {1}{n}
sum_{k=0}^{n-1} f(X_k)$ by means of the Donsker-Varadhan's entropy.
That allows us to obtain the lower bound of large deviations for the
empirical measure $frac {1}{n} sum_{k=0}^{n-1} delta_{X_k}$ in full
generality
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