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

E. Bolthausen

Stochastic Processes and their Applications, 1979, vol. 9, issue 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=[Sigma]nk=1 íi(Xk), then the probability measures induced by {t(n)i/[radical sign]n-[radical sign]n[pi]i}i[epsilon]I([pi]i 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.

Keywords: Central; limit; theorem; weak; convergence; sojourn; times; strongly; ergodic; Markov; chains (search for similar items in EconPapers)
Date: 1979
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