Publication: A central limit theorem for the sojourn times of strongly ergodic Markov chains
A central limit theorem for the sojourn times of strongly ergodic Markov chains
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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. https://doi.org/10.1016/0304-4149(79)90033-4
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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.
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- Bolthausen, E
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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. https://doi.org/10.1016/0304-4149(79)90033-4