On the norming constants occuring in convergent Markov chains

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Abstract
Several theorems concerning the norming constants {aṇ} and {bn} making a normed Markov chain {an (Xn+bn): n ≥ 0} convergent in distribution (or in probability) are given. It is shown that if Rényi's mixing conditions holds, and , whereas in the general case with α ≠ 0 and exists and are finite. Examples regarding maxima of independent and identically distributed random variables, random walk, and branching processes are considered.
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