|
This article is cited in 25 scientific papers (total in 25 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
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:
-
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
   -
Alain-Sol Sznitman, “Martingales dépendant d'un paramètre: une formule d'Ito”, Z Wahrscheinlichkeitstheorie verw Gebiete, 60:1 (1982), 41
-
Harold J. Kushner, “A cautionary note on the use of singular perturbation methods for “small noise” modelst†”, Stochastics, 6:2 (1982), 117
-
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
-
Harold J. Kushner, Paul Dupuis, “Stochastic Approximations via Large Deviations: Asymptotic Properties”, SIAM J Control Optim, 23:5 (1985), 675
-
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
-
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
-
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
-
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
-
A. Yu. Veretennikov, “On the averaging principle for systems of stochastic differential equations”, Math. USSR-Sb., 69:1 (1991), 271–284
-
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
-
A. Yu. Veretennikov, “On Large Deviations for Additive Functionals of Markov Processes I”, Theory Probab Appl, 38:4 (1993), 706
-
Yuri Kifer, “Large deviations, averaging and periodic orbits of dynamical systems”, Commun.Math. Phys, 162:1 (1994), 33
-
A. Yu. Veretennikov, “On large deviations for diffusion processes with measurable coefficients”, Russian Math. Surveys, 50:5 (1995), 977–987
-
V. I. Piterbarg, V. R. Fatalov, “The Laplace method for probability measures in Banach spaces”, Russian Math. Surveys, 50:6 (1995), 1151–1239
-
Yuri Kifer, “Limit theorems in averaging for dynamical systems”, Ergod Th Dynam Sys, 15:6 (1995), 1143
-
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
-
Donald A. Dawson, Michael A. Kouritzin, “Invariance Principles for Parabolic Equations with Random Coefficients”, Journal of Functional Analysis, 149:2 (1997), 377
-
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
-
Agnessa Kovaleva, Leonid Akulenko, “Approximation of Escape Time for Lagrangian Systems With Fast Noise”, IEEE Trans Automat Contr, 52:12 (2007), 2338
 -
N. Abourashchi, A. Yu. Veretennikov, “On stochastic averaging and mixing”, Theory Stoch. Process., 16(32):1 (2010), 111–129
-
KONSTANTINOS SPILIOPOULOS, “FLUCTUATION ANALYSIS AND SHORT TIME ASYMPTOTICS FOR MULTIPLE SCALES DIFFUSION PROCESSES”, Stoch. Dyn, 2013, 1350026
-
Yuri Kifer, S. R. S. Varadhan, “Nonconventional large deviations theorems”, Probab. Theory Relat. Fields, 2013
-
Puhalskii A.A., “On large deviations of coupled diffusions with time scale separation”, Ann. Probab., 44:4 (2016), 3111–3186
 -
N. O. Amelina, O. N. Granichin, A. L. Fradkov, “The method of averaged models for discrete-time adaptive systems”, Autom. Remote Control, 80:10 (2019), 1755–1782
|
| Number of views: |
| This page: | 557 | | Full text: | 223 | | References: | 65 | | First page: | 1 |
|
Terms of Use