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Book Review

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MathSciNet review: 3049874
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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

References [Enhancements On Off] (What's this?)

  • 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
  • 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
  • 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
  • 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
  • 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

Review Information:

Reviewer: Yuri Kifer
Affiliation: Institute of Mathematics, Hebrew University, Jerusalem 91904, Israel
Journal: Bull. Amer. Math. Soc. 50 (2013), 489-493
Published electronically: March 29, 2013
Review copyright: © Copyright 2013 American Mathematical Society