×

On coupling of Markov chains. (English) Zbl 0356.60003


MSC:

60J10 Markov chains (discrete-time Markov processes on discrete state spaces)
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Doeblin, W., Exposé de la theorie des chaÎnes simples constantes de Markov à un nombre fini d’etats, Rev. Math. de l’Union Interbalkanique, 2, 77-105 (1933) · Zbl 0021.42201
[2] Freedman, D., Markov chains (1971), San Francisco: Holden-Day, San Francisco · Zbl 0212.49801
[3] Freedman, D., The Poisson approximation for dependent events, Ann. Probability, 2, 256-269 (1974) · Zbl 0301.60021
[4] Griffeath, D., A maximal coupling for Markov chains, Z. Wahrscheinlichkeitstheorie verw. Gebiete, 31, 95-106 (1975) · Zbl 0301.60043
[5] Griffeath, D.: Coupling methods for Markov processes. Thesis, Cornell University (1975) · Zbl 0301.60043
[6] Griffeath, D.: Uniform coupling of nonhomogeneous Markov chains. [To appear in J. Appl. Probability (1975)] · Zbl 0322.60061
[7] Griffeath, D.: Partial coupling and loss of memory for Markov chains. [To appear in Ann. Probability (1976)] · Zbl 0347.60048
[8] Hodges, J. L.; LeCam, L., The Poisson approximation to the Poisson binomial distribution, Ann. Math. Statist., 31, 737-740 (1960) · Zbl 0100.14301
[9] Jacobsen, M., Pitman, J.W.: Birth, death, and conditioning of Markov chains. [Submitted to Ann. Probability] · Zbl 0363.60052
[10] Orey, S., Limit theorems for Markov chains (1971), London: Van Nostrand, London · Zbl 0295.60054
[11] Pitman, J. W., Uniform rates of convergence for Markov chain transition probabilities, Z. Wahrscheinlichkeitstheorie verw. Gebiete, 29, 193-227 (1974) · Zbl 0373.60077
[12] Pitman, J. W.; Speed, T. P., A note on random times, Stochastic Processes and Their Applications, 1, 369-374 (1973) · Zbl 0275.60060
[13] Serfling, R. J., A general Poisson approximation theorem, Ann. Probability, 3, 726-731 (1975) · Zbl 0321.60018
[14] Vasershtein, L. N., Markov processes on countable product spaces describing large systems of automata, Problemy Peredavci Informacii, 3, 64-72 (1969) · Zbl 0273.60054
[15] Wald, A.; Wolfowitz, J., Two methods of randomization in statistics and the theory of games, Ann. of Math., 53, 581-586 (1951) · Zbl 0042.38401
[16] Williams, D., Path decomposition and continuity of local time for one-dimensional diffusions, Proc. London Math. Soc. 3rd Ser., 28, 738-768 (1975) · Zbl 0326.60093
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.