@article{TVP_2009_54_3_a12,
author = {P. Bertail and S. Cl\'emencon},
title = {Sharp bounds for the tails of functionals of {Markov} chains},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {609--619},
year = {2009},
volume = {54},
number = {3},
language = {en},
url = {http://geodesic.mathdoc.fr/item/TVP_2009_54_3_a12/}
}
P. Bertail; S. Clémencon. Sharp bounds for the tails of functionals of Markov chains. Teoriâ veroâtnostej i ee primeneniâ, Tome 54 (2009) no. 3, pp. 609-619. http://geodesic.mathdoc.fr/item/TVP_2009_54_3_a12/
[1] Bennett S., “Probability inequalities for a sum of independent random variables”, J. Amer. Statist. Assoc., 57 (1962), 33–45 | DOI | Zbl
[2] Bernshtein S. N., “Ob odnom vidoizmenenii neravenstva Chebyshëva i pogreshnosti formuly Laplasa”, Uch. zap. N.-I. kafedry Ukrainy, 1924; Собрание сочинений, т. 4, Наука, М., 1964, 71–80
[3] Bertail P., Clémençon S., “Edgeworth expansions for suitably normalized sample mean statistics of atomic Markov chains”, Probab. Theory Related Fields, 130 (2004), 388–414 | DOI | MR | Zbl
[4] Bolthausen E., “The Berry–Esseen theorem for functionals of discrete Markov chains”, Z. Wahrscheinlichkeitstheor. verw. Geb., 54 (1980), 59–73 | DOI | MR | Zbl
[5] Doukhan P., Mixing: Properties and Examples, Lecture Notes in Statist., 85, Springer-Verlag, Berlin, 1994, 82 pp. | MR | Zbl
[6] Dubinskaite I., “Predelnye teoremy v $\mathbb R^k$. I”, Litov. matem. sb., 22 (1982), 129–140 | Zbl
[7] Dubinskaite I., “Predelnye teoremy v $\mathbb R^k$. II, III”, Litov. matem. sb., 24 (1984), 256–265 ; 325–334 | MR
[8] Fuk D. Kh., Nagaev S. V., “Veroyatnostnye neravenstva dlya summ nezavisimykh sluchainykh velichin”, Teoriya veroyatn. i ee primen., 16:4 (1971), 660–675 ; 21:4 (1976) | MR | Zbl | MR
[9] Glynn P. W., Ormoneit D., “Hoeffding's inequality for uniformly ergodic Markov chains”, Statist. Probab. Lett., 56:2 (2002), 143–146 | DOI | MR | Zbl
[10] Hoeffding W., “Probability inequalities for sums of bounded random variables”, J. Amer. Statist. Assoc., 58 (1963), 13–30 | DOI | MR | Zbl
[11] Léon C. A., Perron F., “Optimal Hoeffding bounds for discrete reversible Markov chains”, Ann. Appl. Probab., 14:2 (2004), 958–970 | DOI | MR | Zbl
[12] Lézaud P., “Chernoff-type bound for finite Markov chains”, Ann. Appl. Probab., 8:3 (1998), 849–867 | DOI | MR | Zbl
[13] Malinovskii V. K., “O predelnykh teoremakh dlya kharrisovskikh tsepei Markova”, Teoriya veroyatn. i ee primen., 31:2 (1986), 315–332 | MR
[14] Marton K., “A measure concentration inequality for contracting Markov chains”, Geom. Funct. Anal., 6:3 (1996), 556–571 | DOI | MR | Zbl
[15] Meyn S. P., Tweedie R. L., Markov Chains and Stochastic Stability, Springer-Verlag London, Ltd., London, 1993, 548 pp. | MR | Zbl
[16] Nagaev S. V., “Umnozhenie predelnykh teorem dlya odnorodnykh tsepei Markova”, Teoriya veroyatn. i ee primen., 6:1 (1961), 67–86 | MR | Zbl
[17] Nagaev S. V., “Large deviations of sums of independent random variables”, Ann. Probab., 7:5 (1979), 745–789 | DOI | MR | Zbl
[18] Nummelin E., “A splitting technique for Harris recurrent chains”, Z. Wahrscheinlichkeitstheor. verw. Geb., 43 (1978), 309–318 | DOI | MR | Zbl
[19] Nummelin E., General Irreducible Markov Chains and Non-negative Operators, Cambridge Univ. Press, Cambridge, 1984, 172 pp. | MR | Zbl
[20] Prokhorov Yu. V., “Rasprostranenie neravenstv S. N. Bernshteina na mnogomernyi sluchai”, Teoriya veroyatn. i ee primen., 13:2 (1968), 266–274 | MR
[21] Rio E., Théorie asymptotique des processus aléatoires faiblement dépendants, Springer-Verlag, Berlin, 2000, 169 pp. | MR
[22] Samson P.-M., “Concentration of measure inequalities for Markov chains and $\Phi$-mixing processes”, Ann. Probab., 28:1 (2000), 416–461 | DOI | MR | Zbl
[23] Smith W. L., “Regenerative stochastic processes”, Proc. Roy. Statist. Soc., Ser. A, 232 (1955), 6–31 | DOI | MR | Zbl
[24] Talagrand M., “The missing factor in Hoeffding's inequalities”, Ann. Inst. H. Poincaré, 31:4 (1995), 689–670 | MR
[25] Thorisson H., Coupling, Stationarity, and Regeneration, Springer-Verlag, New York, 2000, 517 pp. | MR | Zbl