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Bulletin of the American Mathematical Society

The Bulletin publishes expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. The Bulletin also publishes reviews of selected books in mathematics and short articles in the Mathematical Perspectives section, both by invitation only.

ISSN 1088-9485 (online) ISSN 0273-0979 (print)

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.84.

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Book Review

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MathSciNet review: 3049874
Full text of review: PDF   This review is available free of charge.
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?)

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  • 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
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  • 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
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    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