Geodesic
On~rate of mixing and the averaging principle for hypoelliptic stochastic differential equations
Izvestiya. Mathematics , Tome 33 (1989) no. 2, pp. 221-231.

Voir la notice de l'article provenant de la source Math-Net.Ru

Exponential estimates are obtained for the strong mixing coefficient and the coefficient of complete regularity for diffusion processes with degenerate diffusion that are stable in a certain sense. An averaging principle for Itô stochastic equations is obtained with the help of these estimates. Bibliography: 15 titles. 
@article{IM2_1989_33_2_a0,
     author = {A. Yu. Veretennikov},
     title = {On~rate of mixing and the averaging principle for hypoelliptic stochastic differential equations},
     journal = {Izvestiya. Mathematics },
     pages = {221--231},
     publisher = {mathdoc},
     volume = {33},
     number = {2},
     year = {1989},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1989_33_2_a0/}
}
TY  - JOUR
AU  - A. Yu. Veretennikov
TI  - On~rate of mixing and the averaging principle for hypoelliptic stochastic differential equations
JO  - Izvestiya. Mathematics 
PY  - 1989
SP  - 221
EP  - 231
VL  - 33
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_1989_33_2_a0/
LA  - en
ID  - IM2_1989_33_2_a0
ER  - 
%0 Journal Article
%A A. Yu. Veretennikov
%T On~rate of mixing and the averaging principle for hypoelliptic stochastic differential equations
%J Izvestiya. Mathematics 
%D 1989
%P 221-231
%V 33
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_1989_33_2_a0/
%G en
%F IM2_1989_33_2_a0
A. Yu. Veretennikov. On~rate of mixing and the averaging principle for hypoelliptic stochastic differential equations. Izvestiya. Mathematics , Tome 33 (1989) no. 2, pp. 221-231. http://geodesic.mathdoc.fr/item/IM2_1989_33_2_a0/

[1] Kornfeld I. P., Sinai Ya. G., Fomin S. V., Ergodicheskaya teoriya, Nauka, M., 1980 | MR

[2] Venttsel A. D., Freidlin M. I., Fluktuatsii v dinamicheskikh sistemakh pod deistviem malykh sluchainykh vozmuschenii, Nauka, M., 1979 | MR | Zbl

[3] Statulyavichus V. A., “Teoremy bolshikh uklonenii dlya summ zavisimykh sluchainykh velichin, I”, Litovskii matem. sb., XIX:2 (1979), 199–208

[4] Davydov Yu. A., “Usloviya peremeshivaniya dlya tsepei Markova”, Teoriya veroyatnostei i ee primenen., XVIII:2 (1973), 321–338 | MR

[5] Veretennikov A. Yu., “Ob otsenkakh skorosti peremeshivaniya dlya stokhasticheskikh uravnenii Ito”, IV Mezhd. Vilnyus. konf. po teorii veroyatn. i matem. statistike, Tezisy dokladov, t. I, In-t matem. i kibern. AN LitSSR, Vilnyus, 1985, 127–128

[6] Boltkausen E., “The Berry-Esseen theorem for strongly mixing Harris recurrent Markov chains”, Z. Wahrscheinlichkeitstheorie verw. Gebiete, 60 (1982), 283–289 | DOI | MR

[7] Malinovskij V. K., “On some asymptotic relations and identities for Harris recurrent Markov chains”, Statistics and Control of stochastic processes, Steklov seminar, eds. N. V. Kjrylov et al. Optimization Software, Inc., Publ. Division, N.Y., 1984, 317–336 | MR

[8] Khasminskii R. Z., “O printsipe usredneniya dlya stokhasticheskikh differentsialnykh uravnenii Ito”, Kybernetika, 4:3 (1968), 260–279

[9] Griffeath D., “A maximal coupling for Markov chains”, Z. Wahrscheinlichkeitstheorie varw. Gebiete, 31 (1975), 95–106 | DOI | MR | Zbl

[10] Stroock D. W., “The Malliavin calculus and its application to second order parabolic differential equations, I, II”, Math. Systems Theory, 14:1 (1981), 25–65 ; 2, 141–171 | DOI | MR | Zbl | MR | Zbl

[11] Veretennikov A. Yu., “Veroyatnostnye zadachi v teorii gipoelliptichnosti”, Izv. AN. SSSR. Ser. matem., 48:6 (1984), 1151–1170 | MR | Zbl

[12] Stroock D. W., Varadhan S. R. S., “On the support of diffusion processes with applications to the strong maximum principle”, Proceedings of Sixth Berkeley Symp. on Mathematical Statistics and Probability, v. 3, 333–360 | MR

[13] Bony G. M., “Principe du maximum, unicité du problème de Cauchy et inégalite de Harnack pour les operateurs elliptiques degenérés”, Ann. Inst. Fourier, 19 (1969), 277–304 | MR | Zbl

[14] Stroock D. W., Varadhan S. R. S., Multidimension diffusion processes, Springer-Verlag, Berlin et al., 1979 | MR | Zbl

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