@article{TVP_2012_57_1_a1,
author = {A. Yu. Veretennikov and S. A. Klokov},
title = {On local mixing conditions for {SDE} approximations},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {35--61},
year = {2012},
volume = {57},
number = {1},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_2012_57_1_a1/}
}
A. Yu. Veretennikov; S. A. Klokov. On local mixing conditions for SDE approximations. Teoriâ veroâtnostej i ee primeneniâ, Tome 57 (2012) no. 1, pp. 35-61. http://geodesic.mathdoc.fr/item/TVP_2012_57_1_a1/
[1] Borovkov A. A., Ergodichnost i ustoichivost sluchainykh protsessov, URSS/In-t matem., M./Novosibirsk, 1999, 440 pp. | MR
[2] Bkhattachariya R. N., Ranga Rao R., Approksimatsiya normalnym raspredeleniem i asimptoticheskie razlozheniya, Nauka, M., 1982, 286 pp. | MR
[3] Dobrushin R. L., “Tsentralnaya predelnaya teorema dlya neodnorodnykh tsepei Markova. I, II”, Teoriya veroyatn. i ee primen., 1:1 (1956), 72–89 ; 4, 365–425 ; “исправл.”, 3:4 (1958) | MR | Zbl | MR
[4] Dub Dzh. L., Veroyatnostnye protsessy, IL, M., 1956, 605 pp. | MR
[5] Gulinsky O. V., Veretennikov A. Yu., Large Deviations for Discrete-Time Processes with Averaging, VSP, Utrecht, 1993, 186 pp. | MR | Zbl
[6] Ibragimov I. A., Linnik Yu. V., Nezavisimye i statsionarno svyazannye velichiny, Nauka, M., 1965, 524 pp.
[7] Veretennikov A. Yu., Kleptsyna M. L., “Ob ergodicheskikh filtrakh v nepreryvnom vremeni s oshibkoi v nachalnykh dannykh”, Teoriya veroyatn. i ee primen., 53:2 (2008), 240–276
[8] Klokov S. A., “O nizhnikh otsenkakh skorosti peremeshivaniya dlya odnogo klassa markovskikh protsessov”, Teoriya veroyatn. i ee primen., 51:3 (2006), 600–607 | MR | Zbl
[9] Veretennikov A. Yu., Klokov S. A., “O subeksponentsialnoi skorosti peremeshivaniya dlya markovskikh protsessov”, Teoriya veroyatn. i ee primen., 49:1 (2004), 21–35 | MR | Zbl
[10] Klokov S. A., Veretennikov A. Yu., “Sub-exponential mixing rate for a class of Markov processes”, Math. Comm., 9:1 (2004), 9–26 | MR | Zbl
[11] Klokov S. A., Veretennikov A. Yu., “Mixing and convergence rates for a family of Markov processes appriximating SDEs”, Random Oper. Stoch. Equ., 14:2 (2006), 103–126 | DOI | MR | Zbl
[12] Konakov V., Mammen E., “Local limit theorems for transition densities of Markov chains converging to diffusions”, Probab. Theory Related Fields, 117:4 (2000), 551–587 | DOI | MR | Zbl
[13] Krylov N. A., “O vydelenii markovskogo protsessa iz markovskoi sistemy protsessov i postroenii kvazidiffuzionnykh protsessov”, Izv. AN SSSR, 37:3 (1973), 691–708 | MR | Zbl
[14] Lapinskas R., “O lokalnoi predelnoi teoreme i asimptoticheskikh razlozheniyakh v mnogomernom sluchae”, Litov. matem. sb., 11:4 (1971), 817–831 | MR | Zbl
[15] Nummelin E., Obschie neprivodimye tsepi Markova i neotritsatelnye operatory, Mir, M., 1989, 207 pp. | MR
[16] Pitman J. W., “On coupling of Markov chains”, Z. Wahrsceinlichkeitstheor. verw. Geb., 35 (1976), 315–322 | DOI | MR | Zbl
[17] Shervashidze T., Local limit theorems for sums of random variables and parametric estimators of probability density, Dr.Sc. Thesis, N. Muskhelishvili Institute of Computational Mathematics of Georgian Academy of Sciences, Tbilisi, 1999
[18] Statulyavichus V. A., “Predelnye teoremy dlya plotnostei i asimptoticheskie razlozheniya dlya raspredelenii summ nezavisimykh sluchainykh velichin”, Teoriya veroyatn. i ee primen., 10:4 (1965), 645–659
[19] Vasershtein L. N., “Markovskie protsessy na schetnom proizvedenii prostranstv, opisyvayuschie bolshie sistemy avtomatov”, Problemy peredachi informatsii, 5:3 (1969), 64–72 | MR
[20] Veretennikov A. Yu., “Ob otsenkakh skorosti peremeshivaniya dlya stokhasticheskikh differentsialnykh uravnenii”, Teoriya veroyatn. i ee primen., 32:2 (1987), 299–308 | MR
[21] Veretennikov A. Yu., “Ob otsenkakh skorosti peremeshivaniya dlya markovskikh protsessov”, Litov. matem. sb., 31:1 (1991), 40–49 | MR
[22] 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
[23] Veretennikov A. Yu., “O silnykh resheniyakh i yavnykh formulakh dlya reshenii stokhasticheskikh integralnykh uravnenii”, Matem. sb., 111:3 (1980), 434–452 | MR | Zbl
[24] Veretennikov A. Yu., “On lower bounds for mixing coefficients of Markov diffusions”, From Stochastic Calculus to Mathematical Finance. The Shiryaev Festschrift, 2006, 623–633, Springer, Berlin | DOI | MR | Zbl
[25] Sazonov V. V., “On the multi-dimensional central limit theorem”, Sankluj$\bar{\mathrm a}$, 30:2 (1968), 181–204, The Indian Journal of Statistics, Series A | MR