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Wentzell, Alexander Dmitrievich

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Author ID: wentzell.alexander-dmitrievich Recent zbMATH articles by "Wentzell, Alexander Dmitrievich"
Published as: Ventcel’, A.; Ventcel’, A. D.; Venttsel’, A. D.; Venttsel’, Aleksandr Dmitrievich; Venttsel, A. D.; Wentzell, A.; Wentzell, A. D.; Wentzell, Alexander; Wentzell, Alexander D.
External Links: MGP · Math-Net.Ru · Wikidata · GND
Documents Indexed: 69 Publications since 1956, including 13 Books

Publications by Year

Citations contained in zbMATH

43 Publications have been cited 1,473 times in 1,269 Documents Cited by Year
Random perturbations of dynamical systems. Transl. from the Russian by Joseph Szücs. Zbl 0522.60055
Freidlin, M. I.; Wentzell, A. D.
488
1984
Random perturbations of dynamical systems. Transl. from the Russian by Joseph Szuecs. 2nd ed. Zbl 0922.60006
Freidlin, M. I.; Wentzell, A. D.
340
1998
Random perturbations of dynamical systems. Translated from the Russian by J Szücs. 3rd ed. Zbl 1267.60004
Freidlin, Mark I.; Wentzell, Alexander D.
136
2012
On small random perturbations of dynamical systems. Zbl 0297.34053
Ventcel’, A. D.; Freidlin, M. I.
107
1970
Diffusion processes on graphs and the averaging principle. Zbl 0795.60042
Freidlin, Mark I.; Wentzell, Alexander D.
66
1993
Random perturbations of Hamiltonian systems. Zbl 0804.60070
Freidlin, Mark I.; Wentzell, Alexander D.
47
1994
On boundary conditions for multidimensional diffusion processes. Zbl 0089.13404
Ventcel’, A. D.
44
1960
A course in the theory of stochastic processes. Transl. from the Russian by S. Chomet. Foreword by K. L. Chung. Zbl 0502.60001
Wentzell, A. D.
26
1981
Limit theorems on large deviations for Markov stochastic processes. Transl. from the Russian. Zbl 0743.60029
Wentzell, A. D.
25
1990
Diffusion processes on an open book and the averaging principle. Zbl 1075.60100
Freidlin, M. I.; Wentzell, A. D.
22
2004
Long-time behavior of weakly coupled oscillators. Zbl 1119.34044
Freidlin, M. I.; Wentzell, A. D.
19
2006
Averaging principle for stochastic perturbations of multifrequency systems. Zbl 1050.60078
Freidlin, M. I.; Wentzell, A. D.
15
2003
Rough limit theorems on large deviations for Markov stochastic processes. I. Zbl 0361.60005
Ventcel’, A. D.
15
1976
On the asymptotic behavior of the first eigenvalue of a second-order differential operator with small parameter in higher derivatives. Zbl 0364.35046
Ventcel’, A. D.
12
1975
Semi-groups of operators corresponding to a generalized second order differential operator. Zbl 0074.07803
Ventcel’, A. D.
11
1956
Fluctuations in dynamical systems subject to small random perturbations. Zbl 0499.60053
Venttsel’, A. D.; Freĭdlin, M. I.
10
1979
On the asymptotics of eigenvalues of matrices with elements of order \(\exp \{ -V_{ij}/(2 \varepsilon^2) \}\). Zbl 0291.15018
Ventcel’, A. D.
10
1972
Some problems concerning stability under small random perturbations. Zbl 0268.93032
Ventcel’, A. D.; Freidlin, M. I.
10
1972
Reaction-diffusion equations with randomly perturbed boundary conditions. Zbl 0755.35055
Freidlin, Mark I.; Wentzell, Alexander D.
8
1992
Small mass asymptotic for the motion with vanishing friction. Zbl 1260.60160
Freidlin, Mark; Hu, Wenqing; Wentzell, Alexander
7
2013
Necessary and sufficient conditions for weak convergence of one- dimensional Markov processes. Zbl 0820.60058
Freidlin, Mark I.; Wentzell, Alexander D.
6
1994
On the behavior of diffusion processes with traps. Zbl 1411.60042
Freidlin, M.; Koralov, L.; Wentzell, A.
5
2017
On the Neumann problem for PDE’s with a small parameter and the corresponding diffusion processes. Zbl 1243.35184
Freidlin, M. I.; Wentzell, A. D.
5
2012
On the asymptotic behavior of the greatest eigenvalue of a second-order elliptic differential operator with a small parameter in the higher derivatives. Zbl 0241.35060
Ventcel’, A. D.
5
1972
A course in the theory of random processes. 2nd ed. Zbl 0887.60002
Venttsel’, A. D.
4
1996
Rough limit theorems on large deviations for Markov stochastic processes. IV. Zbl 0508.60060
Wentzell, A. D.
4
1982
On diffusions in media with pockets of large diffusivity. Zbl 1422.60043
Freidlin, Mark; Koralov, Leonid; Wentzell, Alexander
2
2019
On the solutions of the equation arising from the singular limit of some eigen problems. Zbl 0920.49015
Sheu, Shuenn-Jyi; Wentzell, Alexander D.
2
1999
Asymptotic expansions in limit theorems for stochastic processes. I. Zbl 0858.60035
Wentzell, A. D.
2
1996
Piecewise constant approximation for the Monte Carlo calculation of Wiener integrals. Zbl 0595.65024
Venttsel’, A. D.; Gladyshev, S. A.; Mil’shtejn, G. N.
2
1985
Theorems on large deviations for stochastic processes. Zbl 0401.60025
Wentzell, A. D.
2
1975
Formulae for eigenfunctions and eigenmeasures associated with a Markov process. Zbl 0287.60067
Ventcel’, A. D.
2
1973
Theorems on the action functional for Gaussian random functions. Zbl 0274.60031
Ventcel’, A. D.
2
1972
Small random perturbations of a dynamical system with a stable equilibrium position. Zbl 0194.48904
Venttsel’, A. D.; Frejdlin, M. I.
2
1969
Non-negative additive functionals of Markov processes. Zbl 0108.15103
Venttsel’, A. D.
2
1961
Some recent results on averaging principle. Zbl 1154.60043
Freidlin, Mark; Wentzell, Alexander
1
2008
Asymptotic expansions in limit theorems for stochastic processes. II. Zbl 0992.60040
Wentzell, Alexander D.
1
1999
Asymptotic problems in probability theory and the theory of random media. Zbl 0724.60031
Venttsel’, A. D.; Molchanov, S. A.; Tutubalin, V. N.
1
1990
Piecewise constant approximation for the Monte Carlo computation of Wiener integrals. Zbl 0582.65016
Venttsel’, A. D.; Gladyshev, S. A.; Mil’shtejn, G. N.
1
1984
Theorie zufälliger Prozesse. In deutscher Sprache hrsg. von Hans Jürgen Engelbert und Jürgen Groh. Zbl 0428.60002
Wentzell, A. D.
1
1979
On the limiting behavior of an invariant measure under small perturbations of a dynamical system. Zbl 0284.60079
Ventcel’, A. D.; Freidlin, M. I.
1
1969
On continuous additive functionals of a multidimensional Wiener process. Zbl 0126.13801
Ventcel’, A.
1
1962
On the absolute continuity of transition probabilities of a one- dimensional diffusion process. Zbl 0115.35904
Venttsel’, A. D.
1
1962
On diffusions in media with pockets of large diffusivity. Zbl 1422.60043
Freidlin, Mark; Koralov, Leonid; Wentzell, Alexander
2
2019
On the behavior of diffusion processes with traps. Zbl 1411.60042
Freidlin, M.; Koralov, L.; Wentzell, A.
5
2017
Small mass asymptotic for the motion with vanishing friction. Zbl 1260.60160
Freidlin, Mark; Hu, Wenqing; Wentzell, Alexander
7
2013
Random perturbations of dynamical systems. Translated from the Russian by J Szücs. 3rd ed. Zbl 1267.60004
Freidlin, Mark I.; Wentzell, Alexander D.
136
2012
On the Neumann problem for PDE’s with a small parameter and the corresponding diffusion processes. Zbl 1243.35184
Freidlin, M. I.; Wentzell, A. D.
5
2012
Some recent results on averaging principle. Zbl 1154.60043
Freidlin, Mark; Wentzell, Alexander
1
2008
Long-time behavior of weakly coupled oscillators. Zbl 1119.34044
Freidlin, M. I.; Wentzell, A. D.
19
2006
Diffusion processes on an open book and the averaging principle. Zbl 1075.60100
Freidlin, M. I.; Wentzell, A. D.
22
2004
Averaging principle for stochastic perturbations of multifrequency systems. Zbl 1050.60078
Freidlin, M. I.; Wentzell, A. D.
15
2003
On the solutions of the equation arising from the singular limit of some eigen problems. Zbl 0920.49015
Sheu, Shuenn-Jyi; Wentzell, Alexander D.
2
1999
Asymptotic expansions in limit theorems for stochastic processes. II. Zbl 0992.60040
Wentzell, Alexander D.
1
1999
Random perturbations of dynamical systems. Transl. from the Russian by Joseph Szuecs. 2nd ed. Zbl 0922.60006
Freidlin, M. I.; Wentzell, A. D.
340
1998
A course in the theory of random processes. 2nd ed. Zbl 0887.60002
Venttsel’, A. D.
4
1996
Asymptotic expansions in limit theorems for stochastic processes. I. Zbl 0858.60035
Wentzell, A. D.
2
1996
Random perturbations of Hamiltonian systems. Zbl 0804.60070
Freidlin, Mark I.; Wentzell, Alexander D.
47
1994
Necessary and sufficient conditions for weak convergence of one- dimensional Markov processes. Zbl 0820.60058
Freidlin, Mark I.; Wentzell, Alexander D.
6
1994
Diffusion processes on graphs and the averaging principle. Zbl 0795.60042
Freidlin, Mark I.; Wentzell, Alexander D.
66
1993
Reaction-diffusion equations with randomly perturbed boundary conditions. Zbl 0755.35055
Freidlin, Mark I.; Wentzell, Alexander D.
8
1992
Limit theorems on large deviations for Markov stochastic processes. Transl. from the Russian. Zbl 0743.60029
Wentzell, A. D.
25
1990
Asymptotic problems in probability theory and the theory of random media. Zbl 0724.60031
Venttsel’, A. D.; Molchanov, S. A.; Tutubalin, V. N.
1
1990
Piecewise constant approximation for the Monte Carlo calculation of Wiener integrals. Zbl 0595.65024
Venttsel’, A. D.; Gladyshev, S. A.; Mil’shtejn, G. N.
2
1985
Random perturbations of dynamical systems. Transl. from the Russian by Joseph Szücs. Zbl 0522.60055
Freidlin, M. I.; Wentzell, A. D.
488
1984
Piecewise constant approximation for the Monte Carlo computation of Wiener integrals. Zbl 0582.65016
Venttsel’, A. D.; Gladyshev, S. A.; Mil’shtejn, G. N.
1
1984
Rough limit theorems on large deviations for Markov stochastic processes. IV. Zbl 0508.60060
Wentzell, A. D.
4
1982
A course in the theory of stochastic processes. Transl. from the Russian by S. Chomet. Foreword by K. L. Chung. Zbl 0502.60001
Wentzell, A. D.
26
1981
Fluctuations in dynamical systems subject to small random perturbations. Zbl 0499.60053
Venttsel’, A. D.; Freĭdlin, M. I.
10
1979
Theorie zufälliger Prozesse. In deutscher Sprache hrsg. von Hans Jürgen Engelbert und Jürgen Groh. Zbl 0428.60002
Wentzell, A. D.
1
1979
Rough limit theorems on large deviations for Markov stochastic processes. I. Zbl 0361.60005
Ventcel’, A. D.
15
1976
On the asymptotic behavior of the first eigenvalue of a second-order differential operator with small parameter in higher derivatives. Zbl 0364.35046
Ventcel’, A. D.
12
1975
Theorems on large deviations for stochastic processes. Zbl 0401.60025
Wentzell, A. D.
2
1975
Formulae for eigenfunctions and eigenmeasures associated with a Markov process. Zbl 0287.60067
Ventcel’, A. D.
2
1973
On the asymptotics of eigenvalues of matrices with elements of order \(\exp \{ -V_{ij}/(2 \varepsilon^2) \}\). Zbl 0291.15018
Ventcel’, A. D.
10
1972
Some problems concerning stability under small random perturbations. Zbl 0268.93032
Ventcel’, A. D.; Freidlin, M. I.
10
1972
On the asymptotic behavior of the greatest eigenvalue of a second-order elliptic differential operator with a small parameter in the higher derivatives. Zbl 0241.35060
Ventcel’, A. D.
5
1972
Theorems on the action functional for Gaussian random functions. Zbl 0274.60031
Ventcel’, A. D.
2
1972
On small random perturbations of dynamical systems. Zbl 0297.34053
Ventcel’, A. D.; Freidlin, M. I.
107
1970
Small random perturbations of a dynamical system with a stable equilibrium position. Zbl 0194.48904
Venttsel’, A. D.; Frejdlin, M. I.
2
1969
On the limiting behavior of an invariant measure under small perturbations of a dynamical system. Zbl 0284.60079
Ventcel’, A. D.; Freidlin, M. I.
1
1969
On continuous additive functionals of a multidimensional Wiener process. Zbl 0126.13801
Ventcel’, A.
1
1962
On the absolute continuity of transition probabilities of a one- dimensional diffusion process. Zbl 0115.35904
Venttsel’, A. D.
1
1962
Non-negative additive functionals of Markov processes. Zbl 0108.15103
Venttsel’, A. D.
2
1961
On boundary conditions for multidimensional diffusion processes. Zbl 0089.13404
Ventcel’, A. D.
44
1960
Semi-groups of operators corresponding to a generalized second order differential operator. Zbl 0074.07803
Ventcel’, A. D.
11
1956
all top 5

Cited by 1,460 Authors

42 Freidlin, Mark I.
20 Bashkirtseva, Irina Adol’fovna
19 Ryashko, Lev Borisovich
15 Cerrai, Sandra
15 Vanden-Eijnden, Eric
13 Duan, Jinqiao
13 Dupuis, Paul G.
13 Koralov, Leonid B.
12 Xi, Fubao
11 Pavlyukevich, Ilya
10 Cameron, Maria Kourkina
10 Day, Martin V.
9 Kifer, Yuri
9 Spiliopoulos, Konstantinos V.
9 Sultanov, Oskar A.
8 Bakhtin, Yuri Yu.
8 Bouchet, Freddy
8 Imkeller, Peter
8 Landim, Claudio
8 Weber, Matthias
8 Wentzell, Alexander Dmitrievich
7 Berglund, Nils
7 Bertini, Lorenzo Bertini
7 Gabrielli, Davide
7 Hu, Wenqing
7 Liu, Jicheng
7 Miclo, Laurent
7 Mikami, Toshio
7 Olivieri, Enzo
7 Salins, Michael
7 Sowers, Richard B.
7 Xu, Yong
6 Bobrowski, Adam
6 Borkar, Vivek Shripad
6 Hairer, Martin
6 Högele, Michael Anton
6 Klebaner, Fima C.
6 Kraaij, Richard Clemens
6 Kühn, Christian
6 Kuksin, Sergeĭ B.
6 Liptser, Robert
6 Pardoux, Etienne
6 Pei, Bin
6 Puhalskii, Anatolii A.
6 Scoppola, Elisabetta
6 Sheu, Shuenn-Jyi
6 Weidenholzer, Simon
5 Brzeźniak, Zdzisław
5 Cerf, Raphaël
5 Chiang, Tzuu-Shuh
5 Dolgopyat, Dmitry
5 E, Weinan
5 Fu, Hongbo
5 Fudenberg, Drew
5 Imhof, Lorens A.
5 Ishii, Hitoshi
5 Jona-Lasinio, Giovanni
5 Korolyuk, Volodymyr Semenovych
5 Kuske, Rachel A.
5 Kutoyants, Yury A.
5 Liu, Xianbin
5 Namachchivaya, N. Sri
5 Newton, Jonathan
5 Novikov, Alexei
5 Pajor-Gyulai, Zsolt
5 Samoilenko, Igor V.
5 Wan, Xiaoliang
5 Yin, George Gang
5 Young, H. Peyton
5 Zambrini, Jean-Claude
5 Zhou, Xiang
4 Agaev, Rafig P.
4 Albeverio, Sergio A.
4 Bovier, Anton
4 Champagnat, Nicolas
4 Chow, Yunshyong
4 Comets, Francis M.
4 Dawson, Donald Andrew
4 Doss, Halim
4 Eizenberg, Alexander
4 Feng, Jin
4 Fleming, Wendell Helms
4 Forgoston, Eric
4 Gagnon, Gregory
4 Gao, Fuqing
4 Gao, Hongjun
4 Gentz, Barbara
4 Giacomin, Giambattista
4 Grafke, Tobias
4 Hartmann, Carsten
4 Holcman, David
4 Iyer, Gautam
4 Lecomte, Vivien
4 Li, Xue-Mei
4 Medvedev, Georgi S.
4 Méléard, Sylvie
4 Qian, Minping
4 Robert, Philippe
4 Röckner, Michael
4 Runolfsson, Thordur
...and 1,360 more Authors
all top 5

Cited in 276 Serials

91 Stochastic Processes and their Applications
81 Journal of Statistical Physics
43 The Annals of Applied Probability
38 The Annals of Probability
36 Probability Theory and Related Fields
30 Journal of Mathematical Analysis and Applications
30 Games and Economic Behavior
26 Physica D
24 Journal of Differential Equations
21 Communications in Mathematical Physics
19 Journal of Economic Theory
19 Chaos
18 Stochastics and Dynamics
17 Statistics & Probability Letters
14 Applied Mathematics and Optimization
14 Journal of Functional Analysis
13 Journal of Theoretical Probability
13 Journal of Nonlinear Science
13 Discrete and Continuous Dynamical Systems
12 Journal of Mathematical Biology
12 Transactions of the American Mathematical Society
12 Stochastic Analysis and Applications
11 Journal of Statistical Mechanics: Theory and Experiment
10 Physics Letters. A
10 Journal of Mathematical Economics
10 Theory of Probability and Mathematical Statistics
9 Journal of Mathematical Physics
9 Stochastics
9 Chaos, Solitons and Fractals
9 Journal of Applied Probability
9 Journal of Economic Dynamics & Control
9 SIAM Journal on Mathematical Analysis
9 Journal of Mathematical Sciences (New York)
9 Annales Henri Poincaré
8 Archive for Rational Mechanics and Analysis
8 Applied Mathematics and Computation
8 European Series in Applied and Industrial Mathematics (ESAIM): Probability and Statistics
8 Multiscale Modeling & Simulation
7 Communications on Pure and Applied Mathematics
7 Journal of Computational Physics
7 Physica A
7 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
7 Theoretical Population Biology
7 Calculus of Variations and Partial Differential Equations
7 Economic Theory
7 Discrete and Continuous Dynamical Systems. Series B
7 Journal of Physics A: Mathematical and Theoretical
6 Advances in Applied Probability
6 Systems & Control Letters
6 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire
6 Queueing Systems
6 Automation and Remote Control
6 Potential Analysis
6 Comptes Rendus. Mathématique. Académie des Sciences, Paris
5 Computers & Mathematics with Applications
5 Journal d’Analyse Mathématique
5 Mathematical Notes
5 Nonlinearity
5 Bulletin of Mathematical Biology
5 Science in China. Series A
5 Communications in Partial Differential Equations
5 Stochastics and Stochastics Reports
5 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
5 Electronic Journal of Probability
5 Communications in Nonlinear Science and Numerical Simulation
5 Frontiers of Mathematics in China
5 Nonlinear Analysis. Theory, Methods & Applications
4 Israel Journal of Mathematics
4 Letters in Mathematical Physics
4 Ukrainian Mathematical Journal
4 Automatica
4 International Journal of Game Theory
4 Journal of Computational and Applied Mathematics
4 Mathematics and Computers in Simulation
4 Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
4 Mathematical and Computer Modelling
4 Journal de Mathématiques Pures et Appliquées. Neuvième Série
4 Journal of Dynamics and Differential Equations
4 Russian Journal of Mathematical Physics
4 Bernoulli
4 Proceedings of the Steklov Institute of Mathematics
4 Science China. Mathematics
3 Journal of the Franklin Institute
3 Journal of Multivariate Analysis
3 Proceedings of the Japan Academy. Series A
3 SIAM Journal on Control and Optimization
3 Acta Applicandae Mathematicae
3 Journal of the American Mathematical Society
3 SIAM Journal on Applied Mathematics
3 SIAM Review
3 Bulletin of the American Mathematical Society. New Series
3 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques
3 Cybernetics and Systems Analysis
3 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI
3 Acta Mathematica Sinica. English Series
3 Physical Review Letters
3 Journal of Nonlinear Mathematical Physics
3 Journal of Evolution Equations
3 Advances in Difference Equations
3 Proceedings of the Japan Academy
...and 176 more Serials
all top 5

Cited in 43 Fields

822 Probability theory and stochastic processes (60-XX)
279 Partial differential equations (35-XX)
159 Ordinary differential equations (34-XX)
146 Dynamical systems and ergodic theory (37-XX)
146 Statistical mechanics, structure of matter (82-XX)
130 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
115 Biology and other natural sciences (92-XX)
91 Systems theory; control (93-XX)
84 Numerical analysis (65-XX)
56 Calculus of variations and optimal control; optimization (49-XX)
53 Fluid mechanics (76-XX)
47 Operator theory (47-XX)
45 Statistics (62-XX)
35 Global analysis, analysis on manifolds (58-XX)
35 Operations research, mathematical programming (90-XX)
31 Mechanics of particles and systems (70-XX)
30 Quantum theory (81-XX)
16 Computer science (68-XX)
11 Combinatorics (05-XX)
11 Functional analysis (46-XX)
11 Classical thermodynamics, heat transfer (80-XX)
10 Geophysics (86-XX)
9 Measure and integration (28-XX)
9 Potential theory (31-XX)
8 Integral equations (45-XX)
8 Information and communication theory, circuits (94-XX)
7 Differential geometry (53-XX)
7 Mechanics of deformable solids (74-XX)
7 Optics, electromagnetic theory (78-XX)
4 Linear and multilinear algebra; matrix theory (15-XX)
4 Difference and functional equations (39-XX)
4 Approximations and expansions (41-XX)
3 Group theory and generalizations (20-XX)
2 Algebraic geometry (14-XX)
2 Real functions (26-XX)
1 General and overarching topics; collections (00-XX)
1 History and biography (01-XX)
1 Topological groups, Lie groups (22-XX)
1 Functions of a complex variable (30-XX)
1 Special functions (33-XX)
1 Harmonic analysis on Euclidean spaces (42-XX)
1 Convex and discrete geometry (52-XX)
1 Relativity and gravitational theory (83-XX)

Citations by Year

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