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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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 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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|Item Type:||Journal Article, refereed, original work|
|Communities & Collections:||07 Faculty of Science > Institute of Mathematics|
|Uncontrolled Keywords:||Central limit theorem; weak convergence; sojourn times; strongly ergodic Markov chains|
|Deposited On:||30 Oct 2009 15:39|
|Last Modified:||23 Nov 2012 13:15|
|Free access at:||Publisher DOI. An embargo period may apply.|
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