Bolthausen, Erwin The Berry-Esseen theorem for functionals of discrete Markov chains. (English) Zbl 0431.60019 Z. Wahrscheinlichkeitstheor. Verw. Geb. 54, 59-73 (1980). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 5 ReviewsCited in 28 Documents MSC: 60F05 Central limit and other weak theorems 60J10 Markov chains (discrete-time Markov processes on discrete state spaces) Keywords:Berry-Esseen theorem for functionals of discrete Markov chains; central limit theorem PDF BibTeX XML Cite \textit{E. Bolthausen}, Z. Wahrscheinlichkeitstheor. Verw. Geb. 54, 59--73 (1980; Zbl 0431.60019) Full Text: DOI OpenURL References: [1] Battacharga, R. N.; Rao, R. R., Normal approximation and asymptotic expansions (1976), New York: Wiley, New York [2] Bolthausen, E., On rates of convergence in a random central limit theorem and in the central limit theorem for Markov chains, Z. Wahrscheinlichkeitstheorie verw. Gebiete, 38, 279-286 (1977) · Zbl 0336.60060 [3] Chung, K. L., Markov chains with stationary transition probabilities (1967), Berlin, Heidelberg, New York: Springer, Berlin, Heidelberg, New York · Zbl 0146.38401 [4] Feller, W., An introduction to probability theory and its applications, Vol. II (1966), New York: Wiley, New York · Zbl 0138.10207 [5] Landers, D.; Rogge, L., The exact approximation order in the central limit theorem for random summation, Z. Wahrscheinlichkeitstheorie verw. Gebiete, 36, 169-183 (1976) · Zbl 0325.60026 [6] Landers, D.; Rogge, L., On the rate of convergence in the central limit theorem for Markov chains, Z. Wahrscheinlichkeitstheorie verw. Gebiete, 35, 169-183 (1976) · Zbl 0315.60014 [7] Lifshits, B. A., On the central limit theorem for Markov chains, Theory Probab. Appl., 23, 279-295 (1978) · Zbl 0422.60052 [8] Pitman, J. W., Uniform rates of convergence for Markov chain transition probabilities, Z. Wahrscheinlichkeitstheorie verw. Gebiete, 29, 193-227 (1974) · Zbl 0373.60077 [9] Pitman, J. W., Occupation measures for Markov chains, Adv. in Appl. Probab., 9, 69-86 (1977) · Zbl 0389.60053 [10] Rosenblatt, M., Markov processes. Structure and asymptotic behaviour (1971), Berlin, Heidelberg, New York: Springer, Berlin, Heidelberg, New York This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.