Book Review
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MathSciNet review:
3049874
Full text of review:
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Book Information:
Authors:
Mark I. Freidlin and
Alexander D. Wentzell
Translated by
Joseph Sz¨ ucs
Title:
Random perturbations of dynamical systems
Additional book information:
Grundlehren der Mathematischen Wissenschaften, Vol. 260,
Springer,
Heidelberg,
3rd ed. edition,
2012,
xxviii+458 pp.,
ISBN 978-3-642-25846-6,
€109.95,
hardcover
M. I. Freĭdlin, The averaging principle and theorems on large deviations, Uspekhi Mat. Nauk 33 (1978), no. 5(203), 107–160, 238 (Russian). MR 511884
Mark I. Freidlin and Alexander D. Wentzell, Random perturbations of Hamiltonian systems, Mem. Amer. Math. Soc. 109 (1994), no. 523, viii+82. MR 1201269, DOI 10.1090/memo/0523
M. I. Freidlin and A. D. Wentzell, Diffusion processes on an open book and the averaging principle, Stochastic Process. Appl. 113 (2004), no. 1, 101–126. MR 2078539, DOI 10.1016/j.spa.2004.03.009
R. Z. Khasminskii, Principle of averaging for parabolic and elliptic differential equations and for Markov processes with small diffusion, Theor. Probab. Appl., 8 (1963), 1–21.
R. Z. Khasminskii, On the averaging principle for Itô stochastic differential equations, Kibernetika (Prague), 4 (1968), 260–279 (in Russian).
Yuri Kifer, Random perturbations of dynamical systems, Progress in Probability and Statistics, vol. 16, Birkhäuser Boston, Inc., Boston, MA, 1988. MR 1015933, DOI 10.1007/978-1-4615-8181-9
Yuri Kifer, A discrete-time version of the Wentzell-Freidlin theory, Ann. Probab. 18 (1990), no. 4, 1676–1692. MR 1071818
Yuri Kifer, Large deviations and adiabatic transitions for dynamical systems and Markov processes in fully coupled averaging, Mem. Amer. Math. Soc. 201 (2009), no. 944, viii+129. MR 2547839, DOI 10.1090/memo/0944
L. S. Pontryagin, A. A. Andronov, and A. A. Vitt, On statistical consideration of dynamical systems, J. Experiment. Theor. Phys., 3 no.1 (1933), 165–180 (in Russian).
A. D. Ventcel′ and M. I. Freĭdlin, Small random perturbations of dynamical systems, Uspehi Mat. Nauk 25 (1970), no. 1 (151), 3–55 (Russian). MR 0267221
References
- M. I. Freĭdlin, The averaging principle and theorems on large deviations, Uspekhi Mat. Nauk 33 (1978), no. 5(203), 107–160, 238 (Russian). MR 511884 (81k:60059)
- Mark I. Freidlin and Alexander D. Wentzell, Random perturbations of Hamiltonian systems, Mem. Amer. Math. Soc. 109 (1994), no. 523, viii+82. MR 1201269 (94j:35064)
- M. I. Freidlin and A. D. Wentzell, Diffusion processes on an open book and the averaging principle, Stochastic Process. Appl. 113 (2004), no. 1, 101–126. MR 2078539 (2005e:60178), DOI 10.1016/j.spa.2004.03.009
- R. Z. Khasminskii, Principle of averaging for parabolic and elliptic differential equations and for Markov processes with small diffusion, Theor. Probab. Appl., 8 (1963), 1–21.
- R. Z. Khasminskii, On the averaging principle for Itô stochastic differential equations, Kibernetika (Prague), 4 (1968), 260–279 (in Russian).
- Yuri Kifer, Random perturbations of dynamical systems, Progress in Probability and Statistics, vol. 16, Birkhäuser Boston Inc., Boston, MA, 1988. MR 1015933 (91e:58159), DOI 10.1007/978-1-4615-8181-9
- Yuri Kifer, A discrete-time version of the Wentzell-Freidlin theory, Ann. Probab. 18 (1990), no. 4, 1676–1692. MR 1071818 (91i:60077)
- Yuri Kifer, Large deviations and adiabatic transitions for dynamical systems and Markov processes in fully coupled averaging, Mem. Amer. Math. Soc. 201 (2009), no. 944, viii+129. MR 2547839 (2011c:60089)
- L. S. Pontryagin, A. A. Andronov, and A. A. Vitt, On statistical consideration of dynamical systems, J. Experiment. Theor. Phys., 3 no.1 (1933), 165–180 (in Russian).
- A. D. Ventcel′ and M. I. Freĭdlin, Small random perturbations of dynamical systems, Uspehi Mat. Nauk 25 (1970), no. 1 (151), 3–55 (Russian). MR 0267221 (42 \#2123)
Review Information:
Reviewer:
Yuri Kifer
Affiliation:
Institute of Mathematics, Hebrew University, Jerusalem 91904, Israel
Email:
kifer@math.huji.ac.il
Journal:
Bull. Amer. Math. Soc.
50 (2013), 489-493
DOI:
https://doi.org/10.1090/S0273-0979-2013-01414-9
Published electronically:
March 29, 2013
Review copyright:
© Copyright 2013
American Mathematical Society