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Book Review
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Book Information
Authors:
Jin Feng;
Thomas G. Kurtz
Title:
Large deviations for stochastic processes
Additional book information
Mathematical Surveys and Monographs, 131,
American Mathematical Society, Providence, R.I.,
2006, xii + 410 pp., US $99.00; All AMS Members: US $79.20, ISBN 978-0-8218-4145-7.
References
- 1.
Julian
D. Cole, On a quasi-linear parabolic equation occurring in
aerodynamics, Quart. Appl. Math. 9 (1951),
225–236. MR 0042889
(13,178c)
- 2.
Amir
Dembo and Ofer
Zeitouni, Large deviations techniques and applications, 2nd
ed., Applications of Mathematics (New York), vol. 38, Springer-Verlag,
New York, 1998. MR 1619036
(99d:60030)
- 3.
Jean-Dominique
Deuschel and Daniel
W. Stroock, Large deviations, Pure and Applied Mathematics,
vol. 137, Academic Press Inc., Boston, MA, 1989. MR 997938
(90h:60026)
- 4.
Paul
Dupuis and Richard
S. Ellis, A weak convergence approach to the theory of large
deviations, Wiley Series in Probability and Statistics: Probability
and Statistics, John Wiley & Sons Inc., New York, 1997. A
Wiley-Interscience Publication. MR 1431744
(99f:60057)
- 5.
W.
H. Fleming and P.
E. Souganidis, A PDE approach to some large deviations
problems, mathematics, Part 1 (Santa Fe, N.M., 1984) Lectures in
Appl. Math., vol. 23, Amer. Math. Soc., Providence, RI, 1986,
pp. 441–447. MR 837690
(87i:60032)
- 6.
Michael
Steven Glass, PERTURBATION OF A FIRST ORDER EQUATION BY A SMALL
DIFFUSION, ProQuest LLC, Ann Arbor, MI, 1970. Thesis (Ph.D.)–New
York University. MR
2619818
- 7.
Eberhard
Hopf, The partial differential equation
𝑢_{𝑡}+𝑢𝑢ₓ=𝜇𝑢ₓₓ,
Comm. Pure Appl. Math. 3 (1950), 201–230. MR 0047234
(13,846c)
- 8.
M.
Schilder, Some asymptotic formulas for Wiener integrals,
Trans. Amer. Math. Soc. 125 (1966), 63–85. MR 0201892
(34 #1770)
- 9.
Adam
Shwartz and Alan
Weiss, Large deviations for performance analysis, Stochastic
Modeling Series, Chapman & Hall, London, 1995. Queues, communications,
and computing; With an appendix by Robert J. Vanderbei. MR 1335456
(96i:60029)
- 10.
V.
Strassen, An invariance principle for the law of the iterated
logarithm, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete
3 (1964), 211–226 (1964). MR 0175194
(30 #5379)
- 11.
S.
R. S. Varadhan, Diffusion processes in a small time interval,
Comm. Pure Appl. Math. 20 (1967), 659–685. MR 0217881
(36 #970)
- 12.
S.
R. S. Varadhan, Large deviations and applications, CBMS-NSF
Regional Conference Series in Applied Mathematics, vol. 46, Society
for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1984. MR 758258
(86h:60067b)
- 13.
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:
S. R. S. Varadhan
Affiliation:
Courant Institute, New York University
Email:
varadhan@cims.nyu.edu
Journal:
Bull. Amer. Math. Soc.
DOI:
http://dx.doi.org/10.1090/S0273-0979-2011-01357-X
PII:
S 0273-0979(2011)01357-X
Posted:
October 26, 2011
Review copyright:
© Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain after
28 years from publication.
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