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Izv. Akad. Nauk SSSR Ser. Mat., 1988, Volume 52, Issue 5, Pages 899–908 (Mi izv1210)  

This article is cited in 6 scientific papers (total in 6 papers)

On rate of mixing and the averaging principle for hypoelliptic stochastic differential equations

A. Yu. Veretennikov


Abstract: 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.

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English version:
Mathematics of the USSR-Izvestiya, 1989, 33:2, 221–231

Bibliographic databases:

UDC: 519.2
MSC: Primary 60H15, 35H05, 60J60; Secondary 47A35
Received: 22.07.1986

Citation: A. Yu. Veretennikov, “On rate of mixing and the averaging principle for hypoelliptic stochastic differential equations”, Izv. Akad. Nauk SSSR Ser. Mat., 52:5 (1988), 899–908; Math. USSR-Izv., 33:2 (1989), 221–231

Citation in format AMSBIB
\Bibitem{Ver88}
\by A.~Yu.~Veretennikov
\paper On~rate of mixing and the averaging principle for hypoelliptic stochastic differential equations
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1988
\vol 52
\issue 5
\pages 899--908
\mathnet{http://mi.mathnet.ru/izv1210}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=972088}
\zmath{https://zbmath.org/?q=an:0677.60057|0664.60060}
\transl
\jour Math. USSR-Izv.
\yr 1989
\vol 33
\issue 2
\pages 221--231
\crossref{https://doi.org/10.1070/IM1989v033n02ABEH000824}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. S. M. Pergamenshchikov, “Asymptotic expansions for a model with distinguished “fast” and “slow” variables, described by a system of singularly perturbed stochastic differential equations”, Russian Math. Surveys, 49:4 (1994), 1–44  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. Susanne Ditlevsen, Michael Sorensen, “Inference for Observations of Integrated Diffusion Processes”, Scand j statist, 31:3 (2004), 417  crossref  mathscinet  zmath  elib
    3. A. Yu. Veretennikov, S. A. Klokov, “On subexponential mixing rate for Markov processes”, Theory Probab. Appl., 49:1 (2005), 110–122  mathnet  crossref  crossref  mathscinet  zmath  isi
    4. N. Abourashchi, A. Yu. Veretennikov, “On stochastic averaging and mixing”, Theory Stoch. Process., 16(32):1 (2010), 111–129  mathnet  mathscinet
    5. Carsten Hartmann, “Balanced model reduction of partially observed Langevin equations: an averaging principle”, Mathematical and Computer Modelling of Dynamical Systems, 17:5 (2011), 463  crossref
    6. A. R. Shirikyan, “Controllability implies mixing. I. Convergence in the total variation metric”, Russian Math. Surveys, 72:5 (2017), 939–953  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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