Geodesic
On law bounds for mixing rates for a class of Markov processes
Teoriâ veroâtnostej i ee primeneniâ, Tome 51 (2006) no. 3, pp. 600-607 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Lower bounds of $\alpha$-mixing rate are established for particular models from a class of stationary Markov processes under recurrence conditions. The bounds are compared to previously known upper bounds of $\beta$-mixing rate in cases of polynomial and subexponential convergence. In the latter case, it is shown that the bounds are sharp.
Keywords: Markov process, recurrence, invariant measure, mixing coefficients, subexponential rate.
Mots-clés : polynomial rate 
@article{TVP_2006_51_3_a9,
     author = {S. A. Klokov},
     title = {On law bounds for mixing rates for a class of {Markov} processes},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {600--607},
     year = {2006},
     volume = {51},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2006_51_3_a9/}
}
TY  - JOUR
AU  - S. A. Klokov
TI  - On law bounds for mixing rates for a class of Markov processes
JO  - Teoriâ veroâtnostej i ee primeneniâ
PY  - 2006
SP  - 600
EP  - 607
VL  - 51
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TVP_2006_51_3_a9/
LA  - ru
ID  - TVP_2006_51_3_a9
ER  - 
%0 Journal Article
%A S. A. Klokov
%T On law bounds for mixing rates for a class of Markov processes
%J Teoriâ veroâtnostej i ee primeneniâ
%D 2006
%P 600-607
%V 51
%N 3
%U http://geodesic.mathdoc.fr/item/TVP_2006_51_3_a9/
%G ru
%F TVP_2006_51_3_a9
S. A. Klokov. On law bounds for mixing rates for a class of Markov processes. Teoriâ veroâtnostej i ee primeneniâ, Tome 51 (2006) no. 3, pp. 600-607. http://geodesic.mathdoc.fr/item/TVP_2006_51_3_a9/

[1] Bradley R. C., “Counterexamples to the central limit theorem under strong mixing conditions”, Colloq. Math. Soc. János Bolyai, 36, 1984, 153–172 | MR | Zbl

[2] Bradley R. C., “Basic properties of strong mixing conditions”, Progr. Probab. Statist., 11 (1986), 165–192 | MR | Zbl

[3] Bradley R. C., “Identical mixing rates”, Probab. Theory Related Fields, 74:4 (1987), 497–503 | DOI | MR | Zbl

[4] Bradley R. C., “Counterexamples to the central limit theorem under strong mixing conditions. II”, Colloq. Math. Soc. János Bolyai, 57, 1990, 59–67 | MR | Zbl

[5] Davydov Yu. A., “Usloviya peremeshivaniya dlya tsepei Markova”, Teoriya veroyatn. i ee primen., 18:2 (1973), 321–338 | MR | Zbl

[6] Dub Dzh. L., Veroyatnostnye protsessy, IL, M., 1956, 605 pp. | MR

[7] Doukhan P., Massart P., Rio E., “The functional central limit theorem for strongly mixing processes”, Ann. Inst. H. Poincaré, 30:1 (1994), 63–82 | MR | Zbl

[8] Grin A. G., “Predelnye teoremy dlya skhemy serii slabo zavisimykh velichin”, Teoriya veroyatn. i ee primen., 40:4 (1995), 888–897 | MR | Zbl

[9] Ibragimov I. A., Linnik Yu. V., Nezavisimye i statsionarno svyazannye velichiny, Nauka, M., 1965, 524 pp.

[10] Klokov S. A., Veretennikov A. Yu., “Sub-exponential mixing rate for a class of Markov chains”, Math. Commun., 9:1 (2004), 9–26 | MR | Zbl

[11] Malyshkin M. N., “Subeksponentsialnye otsenki skorosti skhodimosti k invariantnoi mere dlya stokhasticheskikh differentsialnykh uravnenii”, Teoriya veroyatn. i ee primen., 45:3 (2000), 489–504 | MR | Zbl

[12] Merlevède F., Peligrad M., “The functional central limit theorem under the strong mixing condition”, Ann. Probab., 28:3 (2000), 1336–1352 | DOI | MR | Zbl

[13] Meyn S. P., Tweedie R. L., Markov Chains and Stochastic Stability, Springer-Verlag, London, 1993, 548 pp. | MR | Zbl

[14] Rosenblatt M., “A central limit theorem and a strong mixing condition”, Proc. Natl. Acad. Sci. USA, 42 (1956), 43–47 | DOI | MR | Zbl

[15] Veretennikov A. Yu., “Ob otsenkakh skorosti peremeshivaniya dlya stokhasticheskikh uravnenii”, Teoriya veroyatn. i ee primen., 32:2 (1987), 299–308 | MR

[16] Veretennikov A. Yu., “O polinomialnom peremeshivanii i skorosti skhodimosti dlya stokhasticheskikh differentsialnykh i raznostnykh uravnenii”, Teoriya veroyatn. i ee primen., 44:2 (1999), 312–327 | MR | Zbl