Keywords
- Markov Chain
- Limit Theorem
- Central Limit Theorem
- Regenerative Method
- Remainder Term
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, access via your institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Aleshkevichiene A. On limit theorems for the renewal processes.-Litovs.Matem.Sbornik, 1971, v. 11, N 1, p. 19–25 (in Russian).
Athreya K.B., McDonald D., Ney P. Limit theorems for semi-Markov processes and renewal theory for Markov chains.-Ann.Probab., 1978, v. 6, N 5, p. 788–797.
Bikelis A. Zum zentralen Grenzwertsatz in RK.-Chalmers Inst. of Technol. and the University of Goeteborg, 1972, N 9, p. 14–21.
Bikelis A. On the central limit theorem in RK, I — III.-Litovs.Matem.Sbornik, 1971, v. 11, N 1, p. 27–58; 1972, v. 12, N 2, p. 73–84; 1972, v. 12, p. 19–35 (in Russian).
Bhattacharya R., Ranga Rao R. Normal approximation and asymptotic expansions.-New York etc.: Wiley, 1976, 274 p.
Bolthausen E. On rates of convergence in a random central limit theorem and the central limit theorem for Markov chains.-Z. Wahrscheinlichkeitstheorie verw. Gebiete, 1977, Bd. 38, S. 279–286.
Bolthausen E. The Berry-Esseen theorem for functionals of discrete Markov chains.-Z. Wahrscheinlichkeitstheorie verw. Gebiete, 1980, Bd. 54, S. 39–73.
Bolthausen E. The Berry-Esseen theorem for strongly mixing Harris recurrent Markov chains.-Z. Wahrscheinlichkeitstheorie verw.Gebiete, 1982, Bd. 60, S. 283–289.
Chung K.L. Markov chains with stationary transition probabilities. 2nd ed. Berlin etc.: Springer, 1967, 301 p.
Doeblin W. Sur deux problèmes de M.Kolmogoroff concertant les chaînes dénombrables.-Bull.Soc.Math. de France, 1938, v. 66, p. 210–220.
Doob J.L. Stochastic processes. Chichester etc.; Wiley, 1966, 645 p.
Davydor Yu.A. Mixing conditions for Markov chains.-Theorija verojatn. i primen., 1973, v. 18, N 2, p. 321–338 (in Russian).
Dubinskaite J. Asymptotic expansions in the local limit theorem for the sums of independent m-lattice random vectors.-Litovs.Matem.Sbornik, 1978, v. 18, N 4, p. 21–34; 1979, v. 19, N 1, p. 57–66 (in Russian).
Duflo M. Opérateurs potentiels des chaines et des processus de Markov irréductibles.-Bull.Soc.Math. de France, 1970, v. 98, p. 127–163.
Kalashnikov V.V. The qualitive analysis of complex systems by the testing functions method. Moscow, Nauka, 1978, 248 p. (in Russian).
Kalashnikov V.V. Property of γ-reflexivity for Markovian sequences.-Dokl.Akademii Nauk SSSR, 1973, v. 213, N 6, p. 1243–1246. (in Russian).
Kolmogoroff A.N. Markov chains with denumerable state space.-Bull. of Moscow University, 1937, v. 1, N 3 (in Russian).
Kolmogoroff A.N. The local limit theorem for classical Markov chains.-Isv.Akademii Nauk SSSR, ser. math., 1949, v. 13, p. 281–300 (in Russian).
Korolyuk V.S., Turbin A.F. Markov renewal processes in problems of reliability of systems. Kiev, Naukova dumka, 1982, 235 p. (in Russian).
Landers D., Rogge L. On the rate of convergence in the central limit theorem for Markov chains.-Z.Wahrscheinlichkeitstheorie verw. Gebiete, 1976, Bd. 35, S. 57–63.
Malinovsky V.K. On the deficiency of the asymptotically efficient test calculation in the case of Markov observations.-Dokl.Akademii Nauk SSSR, 1982, v. 267, N 5, p. 1053–1057 (in Russian).
Malinovsky V.K. On asymptotic expansions in central limit theorem for Harris recurrent Markov chains.-Dokl.Akademii Nauk SSSR, 1984, v. 276, N 6, p. 1304–1309 (in Russian).
Nagaev A.V. The local limit theorem for the number of renewals.-Litovs.Matem.Sbornik, 1970, v. 10, N 1, p. 109–119 (in Russian).
Nummelin E. A splitting technique for Harris recurrent Markov chains.-Z.Wahrscheinlichkeitstheorie verw. Gebiete, 1978, Bd. 43, S. 309–318.
Nummelin E. Uniform and ratio limit theorems for Markov renewal and semi-regenerative processes on a general state space.-Ann. Inst. Poincaré, Sect. B., 1978, v. 14, N 2, p. 119–143.
Orey S. Lecture notes on the limit theorems for Markov chain transition probabilities. New York etc.: Van Nostrand, 1971, 108 p.
Revuz D. Markov chains. Amsterdam etc.: North Holland, 1975, 336 p.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1985 Springer-Verlag
About this paper
Cite this paper
Malinovsky, V.K. (1985). On limit theorems for the number of Markov renewals. In: Kalashnikov, V.V., Zolotarev, V.M. (eds) Stability Problems for Stochastic Models. Lecture Notes in Mathematics, vol 1155. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0074820
Download citation
DOI: https://doi.org/10.1007/BFb0074820
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-15985-8
Online ISBN: 978-3-540-39686-4
eBook Packages: Springer Book Archive
