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A central limit theorem for the sojourn times of strongly ergodic Markov chains


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.

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.

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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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Uncontrolled Keywords:Central limit theorem; weak convergence; sojourn times; strongly ergodic Markov chains
Language:English
Date:November 1979
Deposited On:30 Oct 2009 15:39
Last Modified:05 Apr 2016 13:30
Publisher:Elsevier
ISSN:0304-4149
Free access at:Publisher DOI. An embargo period may apply.
Publisher DOI:10.1016/0304-4149(79)90033-4
Related URLs:http://www.zentralblatt-math.org/zbmath/search/?q=an%3A0412.60027

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