Geodesic
On subexponential mixing rate for Markov processes
Teoriâ veroâtnostej i ee primeneniâ, Tome 49 (2004) no. 1, pp. 21-35 Cet article a éte moissonné depuis la source Math-Net.Ru

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This paper establishes subexponential bounds for the $t$-mixing and the rate of convergence to invariant measure for homogeneous Markov processes with continuous and discrete time.
Keywords: Markov process, mixing, convergence to the equilibrium. 
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A. Yu. Veretennikov; S. A. Klokov. On subexponential mixing rate for Markov processes. Teoriâ veroâtnostej i ee primeneniâ, Tome 49 (2004) no. 1, pp. 21-35. http://geodesic.mathdoc.fr/item/TVP_2004_49_1_a1/

[1] Ganidis H., Roynette B., Simonot F., “Convergence rate of some semi-groups to their invariant probability”, Stochastic Process. Appl., 79:2 (1999), 243–263 | DOI | MR | Zbl

[2] Guillin A., “Moderate deviations of inhomogeneous functionals of Markov processes and application to averaging”, Stochastic Process. Appl., 92:2 (2001), 287–313 | DOI | MR | Zbl

[3] Dub Dzh. L., Veroyatnostnye protsessy, IL, M., 1956, 604 pp.

[4] Kalashnikov V. V., “Svoistvo $\gamma$-vozvratnosti dlya markovskikh posledovatelnostei”, Dokl. AN SSSR, 213:6 (1973), 1243–1246 | Zbl

[5] Kalashnikov V. V., Kachestvennyi analiz povedeniya slozhnykh sistem metodom probnykh funktsii, Nauka, M., 1978, 247 pp. | MR

[6] Khasminskii R. Z., Ustoichivost sistem differentsialnykh uravnenii pri sluchainykh vozmuscheniyakh ikh parametrov, Nauka, M., 1969, 367 pp. | MR

[7] Krylov N. V., Safonov M. V., “Ob odnom svoistve reshenii parabolicheskikh uravnenii s izmerimymi koeffitsientami”, Izv. AN SSSR, ser. matem., 44:1 (1980), 161–175 | MR | Zbl

[8] Ladyzhenskaya O. A., Solonnikov V. A., Uraltseva N. N., Lineinye i kvazilineinye uravneniya parabolicheskogo tipa, Nauka, M., 1967, 736 pp. | MR

[9] Lamperti J., “Criteria for stochastic processes. II. Passage-time moments”, J. Math. Anal. Appl., 7 (1963), 127–145 | DOI | MR | Zbl

[10] 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

[11] Pardoux E., Veretennikov A. Yu., “On the Poisson equation and diffusion approximation. I”, Ann. Probab., 29:3 (2001), 1061–1085 | DOI | MR | Zbl

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

[13] Veretennikov A. Yu., “O skorosti peremeshivaniya i printsipe usredneniya dlya gipoellipticheskikh stokhasticheskikh differentsialnykh uravnenii”, Izv. AN SSSR, ser. matem., 52:5 (1988), 899–908 | MR | Zbl

[14] Veretennikov A. Yu., Gulinskii O. V., “O skorosti peremeshivaniya i printsipe usredneniya dlya stokhasticheskikh rekurrentnykh protsedur”, Avtomat. i telemekh., 1990, no. 6, 68–78 | MR | Zbl

[15] Veretennikov A. Yu., “Ob otsenkakh skorosti peremeshivaniya dlya markovskikh protsessov”, Litov. matem. sb., 31:1 (1991), 40–49 | MR

[16] Veretennikov A. Yu., “On polynomial mixing bounds for stochastic differential equations”, Stochastic Process. Appl., 70:1 (1997), 115–127 | DOI | MR | Zbl

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