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A central limit theorem for the sojourn times of strongly ergodic Markov chains. (English) Zbl 0412.60027


MSC:

60F05 Central limit and other weak theorems
60J65 Brownian motion
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[1] Baxter, J. R.; Brosamler, G. A., Energy and the law of iterated logarithm, Math. Scand., 38, 115-136 (1976) · Zbl 0346.60020
[2] E. Bolthausen, On the global asymptotic behavior of Brownian local time on the circle, Trans. Am. Math. Soc., to appear.; E. Bolthausen, On the global asymptotic behavior of Brownian local time on the circle, Trans. Am. Math. Soc., to appear. · Zbl 0413.60012
[3] Chung, K. L., (Markov Chains with Stationary Transition Probabilities (1967), Springer: Springer Berlin) · Zbl 0121.12901
[4] Gebelein, H., Das statistische Problem der Korrelation als Variations- und Eigenwertproblem und sein Zusammenhang mit der Ausgleichsrechnung, Z. Angew. Math. Mech., 21, 364-371 (1941) · JFM 67.0491.01
[5] Kemeny, J. G.; Snell, J. L.; Knapp, A. W., Denumerable Markov Chains (1976), Springer: Springer New York · Zbl 0149.13301
[6] Parthasaraty, K. R., Probability Measures on Metric Spaces (1967), Academic Press: Academic Press New York
[7] Pitman, J. W., Uniform rates of convergence for Markov chain transition probabilities, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, 29, 193-227 (1974) · Zbl 0373.60077
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