RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor
Subscription
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Uspekhi Mat. Nauk:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Uspekhi Mat. Nauk, 1978, Volume 33, Issue 5(203), Pages 107–160 (Mi umn3522)  

This article is cited in 24 scientific papers (total in 24 papers)

The averaging principle and theorems on large deviations

M. I. Freidlin


Full text: PDF file (3090 kB)
References: PDF file   HTML file

English version:
Russian Mathematical Surveys, 1978, 33:5, 117–176

Bibliographic databases:

UDC: 517.9
MSC: 34C29, 34A40, 34C10
Received: 29.11.1977

Citation: M. I. Freidlin, “The averaging principle and theorems on large deviations”, Uspekhi Mat. Nauk, 33:5(203) (1978), 107–160; Russian Math. Surveys, 33:5 (1978), 117–176

Citation in format AMSBIB
\Bibitem{Fre78}
\by M.~I.~Freidlin
\paper The averaging principle and theorems on~large deviations
\jour Uspekhi Mat. Nauk
\yr 1978
\vol 33
\issue 5(203)
\pages 107--160
\mathnet{http://mi.mathnet.ru/umn3522}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=511884}
\zmath{https://zbmath.org/?q=an:0407.60015|0416.60029}
\transl
\jour Russian Math. Surveys
\yr 1978
\vol 33
\issue 5
\pages 117--176
\crossref{https://doi.org/10.1070/RM1978v033n05ABEH002516}


Linking options:
  • http://mi.mathnet.ru/eng/umn3522
  • http://mi.mathnet.ru/eng/umn/v33/i5/p107

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. B. Minasyan, “An averaging principle and a theorem on large deviations for a family of extensions of a $Y$-flow”, Russian Math. Surveys, 35:2 (1980), 251–252  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. Alain-Sol Sznitman, “Martingales dépendant d'un paramètre: une formule d'Ito”, Z Wahrscheinlichkeitstheorie verw Gebiete, 60:1 (1982), 41  crossref  mathscinet  zmath  isi
    3. Harold J. Kushner, “A cautionary note on the use of singular perturbation methods for “small noise” modelst†”, Stochastics, 6:2 (1982), 117  crossref
    4. Harold J. Kushner, “Robustness and Approximation of Escape Times and Large Deviations Estimates for Systems with Small Noise Effects”, SIAM J Appl Math, 44:1 (1984), 160  crossref  mathscinet  zmath  isi
    5. Harold J. Kushner, Paul Dupuis, “Stochastic Approximations via Large Deviations: Asymptotic Properties”, SIAM J Control Optim, 23:5 (1985), 675  crossref  mathscinet  zmath  isi
    6. Paul Dupuis, Harold J. Kushner, “Large Deviations Estimates for Systems with Small Noise Effects, and Applications to Stochastic Systems Theory”, SIAM J Control Optim, 24:5 (1986), 979  crossref  mathscinet  zmath  isi
    7. H. J. Kushner, “Asymptotic Global Behavior for Stochastic Approximation and Diffusions with Slowly Decreasing Noise Effects: Global Minimization via Monte Carlo”, SIAM J Appl Math, 47:1 (1987), 169  crossref  mathscinet  zmath  isi
    8. P. Dupuis, H. J. Kushner, “Stochastic Systems with Small Noise, Analysis and Simulation; A Phase Locked Loop Example”, SIAM J Appl Math, 47:3 (1987), 643  crossref  mathscinet  zmath  isi
    9. Paul Dupuis, Harold J. Kushner, “Stochastic Approximation and Large Deviations: Upper Bounds and w.p.1 Convergence”, SIAM J Control Optim, 27:5 (1989), 1108  crossref  mathscinet  zmath  isi
    10. A. Yu. Veretennikov, “On the averaging principle for systems of stochastic differential equations”, Math. USSR-Sb., 69:1 (1991), 271–284  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    11. A. Yu. Veretennikov, “On large deviations in the averaging principle for stochastic differential equations with periodic coefficients. II”, Math. USSR-Izv., 39:1 (1992), 677–701  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    12. A. Yu. Veretennikov, “On Large Deviations for Additive Functionals of Markov Processes I”, Theory Probab Appl, 38:4 (1993), 706  mathnet  crossref  mathscinet  zmath  isi
    13. Yuri Kifer, “Large deviations, averaging and periodic orbits of dynamical systems”, Commun.Math. Phys, 162:1 (1994), 33  crossref
    14. A. Yu. Veretennikov, “On large deviations for diffusion processes with measurable coefficients”, Russian Math. Surveys, 50:5 (1995), 977–987  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    15. V. I. Piterbarg, V. R. Fatalov, “The Laplace method for probability measures in Banach spaces”, Russian Math. Surveys, 50:6 (1995), 1151–1239  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    16. Yuri Kifer, “Limit theorems in averaging for dynamical systems”, Ergod Th Dynam Sys, 15:6 (1995), 1143  crossref
    17. K. NAJIM, A. RUSNAK, A. MESZAROS, M. FIKAR, “Constrained long-range predictive control based on artificial neural networks”, International Journal of Systems Science, 28:12 (1997), 1211  crossref
    18. Donald A. Dawson, Michael A. Kouritzin, “Invariance Principles for Parabolic Equations with Random Coefficients”, Journal of Functional Analysis, 149:2 (1997), 377  crossref
    19. Ludwig Arnold, Peter Imkeller, Yonghui Wu‡, “Reduction of deterministic coupled atmosphere–ocean models to stochastic ocean models: a numerical case study of the Lorenz–Maas system”, Dynamical Systems, 18:4 (2003), 295  crossref
    20. Agnessa Kovaleva, Leonid Akulenko, “Approximation of Escape Time for Lagrangian Systems With Fast Noise”, IEEE Trans Automat Contr, 52:12 (2007), 2338  crossref  mathscinet  isi  elib
    21. N. Abourashchi, A. Yu. Veretennikov, “On stochastic averaging and mixing”, Theory Stoch. Process., 16(32):1 (2010), 111–129  mathnet  mathscinet
    22. KONSTANTINOS SPILIOPOULOS, “FLUCTUATION ANALYSIS AND SHORT TIME ASYMPTOTICS FOR MULTIPLE SCALES DIFFUSION PROCESSES”, Stoch. Dyn, 2013, 1350026  crossref
    23. Yuri Kifer, S. R. S. Varadhan, “Nonconventional large deviations theorems”, Probab. Theory Relat. Fields, 2013  crossref
    24. Puhalskii A.A., “On large deviations of coupled diffusions with time scale separation”, Ann. Probab., 44:4 (2016), 3111–3186  crossref  mathscinet  zmath  isi  elib  scopus
  • Успехи математических наук Russian Mathematical Surveys
    Number of views:
    This page:526
    Full text:205
    References:61
    First page:1

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019