The Limiting Distribution of Maxima of Random Variables Defined on a Denumerable Markov Chain
George L. O’Brien · The Annals of Probability · 1974
Gnedenko's work (1943) showing the existence of a limiting distribution for the maximum of the first $n$ terms in a sequence of suitably normalized independent identically distributed random variables is extended to sequences of random variables defined on a positive-recurrent denumerable Markov chain.