Abstract
Let {X n } n≥0 be a Harris recurrent Markov chain with state space E, transition probability P(x, A) and invariant measure π, and let f be a real measurable function on E. We prove that with probability one,
under some best possible conditions.
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Chen, X. The Law of the Iterated Logarithm for Functionals of Harris Recurrent Markov Chains: Self Normalization. Journal of Theoretical Probability 12, 421–445 (1999). https://doi.org/10.1023/A:1021630228280
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DOI: https://doi.org/10.1023/A:1021630228280