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# Bolthausen, E (1979). A central limit theorem for the sojourn times of strongly ergodic Markov chains. Stochastic Processes and their Applications, 9(2):217-222.

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## Abstract

Let Xn be an irreducible aperiodic recurrent Markov chain with countable state space I and with the mean recurrence times having second moments. There is proved a global central limit theorem for the properly normalized sojourn times. More precisely, if t(n)i=Σnk=1 íi(Xk), then the probability measures induced by {t(n)i/√n−√nπi}iεI(πi being the ergotic distribution) on the Hilbert-space of square summable I-sequences converge weakly in this space to a Gaussian measure determined by a certain weak potential operator.