Large deviations and strong mixing
Bryc, Włodzimierz ; Dembo, Amir
Annales de l'I.H.P. Probabilités et statistiques, Tome 32 (1996), p. 549-569 / Harvested from Numdam
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@article{AIHPB_1996__32_4_549_0,
     author = {Bryc, W\l odzimierz and Dembo, Amir},
     title = {Large deviations and strong mixing},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     volume = {32},
     year = {1996},
     pages = {549-569},
     zbl = {0863.60028},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPB_1996__32_4_549_0}
}

Bryc, Włodzimierz; Dembo, Amir. Large deviations and strong mixing. Annales de l'I.H.P. Probabilités et statistiques, Tome 32 (1996) pp. 549-569. http://gdmltest.u-ga.fr/item/AIHPB_1996__32_4_549_0/

[1] J.R. Baxter, N.C. Jain and S.R.S. Varadhan, Some familiar examples for which the large deviation principle does not hold, Commun. Pure Appl. Math., Vol. 34, 1991, pp. 911-923. | MR 1127039 | Zbl 0749.60025

[2] E. Bolthausen and U. Schmock, On the maximum entropy principle for uniformly ergodic Markov chains, Stochastic Processes Appl., Vol. 33, 1989, pp. 1-27. | MR 1027105 | Zbl 0691.60023

[3] R.C. Bradley, Basic properties of strong mixing conditions. In E. EBERLEIN and M. TAQQU, eds., Dependence in Probability and Statistics, Birkhäuser, Basel, Switzerland, 1986, pp. 165-192. | MR 899990 | Zbl 0603.60034

[4] R.C. Bradley, W. Bryc and S. Janson, On dominations between measures of dependence, J. Multivar. Anal., Vol. 23, 1987, pp. 312-329. | MR 918261 | Zbl 0627.60009

[5] R.C. Bradley and M. Peligrad, Invariance principles under a two-part mixing assumption, Stochastic Processes Appl., Vol. 22, 1986, pp. 271-289. | MR 860937 | Zbl 0609.60048

[6] W. Bryc, On large deviations for uniformly strong mixing sequences, Stochastic Processes Appl., Vol. 41, 1992, pp. 191-202. | MR 1164173 | Zbl 0756.60027

[7] W. Bryc and W. Smolenski, On the convergence of averages of mixing sequences, J. Theor. Probab., Vol. 6, 1993, pp. 473-483. | MR 1230342 | Zbl 0776.60035

[8] T. Chiyonobu and S. Kusuoka, The large deviation principle for hypermixing processes, Probab. Theory Relat. Fields, Vol. 78, 1988, pp. 627-649. | MR 950350 | Zbl 0634.60025

[9] D. Dawson and J. Gärtner, Large deviations from the McKean-Vlasov limit for weakly interacting diffusions, Stochastics, Vol. 20, 1987, pp. 247-308. | MR 885876 | Zbl 0613.60021

[10] A. De Acosta, Large deviations for empirical measures of Markov chains, J. Theor. Probab., Vol. 3, 1990, pp. 395-431. | MR 1057523 | Zbl 0711.60023

[11] A. De Acosta, On large deviations of empirical measures in τ topology, special issue of Journal of Applied Probability in honor of L. TAKACS, Vol. 31A, 1994, pp. 41-47. | MR 1274716 | Zbl 0810.60022

[12] A. Dembo and O. Zeitouni, Large Deviations Techniques and Applications, Jones and Bartlett, Boston, MA, 1993. | MR 1202429 | Zbl 0793.60030

[13] J.D. Deuschel and D.W. Stroock, Large Deviations, Academic Press, Boston, MA, 1989. | MR 997938 | Zbl 0705.60029

[14] I.H. Dinwoodie, Identifying a large deviation rate function, Ann. Probab., Vol. 21, 1993, pp. 216-231. | MR 1207224 | Zbl 0777.60024

[15] I.H. Dinwoodie and S.L. Zabell, Large deviations for exchangeable random vectors, Ann. Probab., Vol. 20, 1992, pp. 1147-1166. | MR 1175254 | Zbl 0760.60025

[16] M.D. Donsker and S.R.S. Varadhan, Asymptotic evaluation of certain Markov process expectations for large time, I, Commun. Pure Appl. Math., Vol. 28, 1975, pp. 1-47. | MR 386024 | Zbl 0323.60069

[17] M.D. Donsker and S.R.S. Varadhan, Asymptotic evaluation of certain Markov process expectations for large time, III. Commun. Pure Appl. Math., Vol. 29, 1976, pp. 389-461. | MR 428471 | Zbl 0348.60032

[18] J.L. Doob, Stochastic Processes, Wiley, New York, NY, 1953. | MR 58896 | Zbl 0053.26802

[19] J.M. Hammersley, Generalization of the fundamental theorem on subadditive functions, Math. Proc. Camb. Philos. Soc., Vol. 58, 1962, pp. 235-238. | MR 137800 | Zbl 0121.29402

[20] N.C. Jain, Large deviation lower bounds for additive functionals of Markov processes, Ann. Probab., Vol. 18, 1990, pp. 1071-1098. | MR 1062059 | Zbl 0713.60037

[21] P. Ney and E. Nummelin, Markov additive processes II: large deviations, Ann. Probab., Vol. 15, 1987, pp. 593-609. | MR 885132 | Zbl 0625.60028

[22] H. Yijun, Large deviations for stationary φ-mixing sequences in r-topology, preprint 1993.

[23] E. Nummelin, General irreducible Markov chains and non-negative operators, Cambridge Tracts in Mathematics, Vol. 83, Cambridge University Press, 1984. | MR 776608 | Zbl 0551.60066

[24] E. Nummelin, Large deviations for functionals of stationary processes, Probab. Theory Relat. Fields, Vol. 86, 1990, pp. 387-401. | MR 1069286 | Zbl 0685.60029

[25] G.L. O'Brien, Sequences of capacities, with connections to large-deviation theory, J. Theoretical Probab., Vol. 8, 1995. | Zbl 0847.60061

[26] M. Rosenblatt, Markov Processes, Structure and Asymptotic Behavior, Springer-Verlag, Berlin, 1971. | MR 329037 | Zbl 0236.60002