Book Review
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MathSciNet review:
2985958
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Book Information:
Authors:
Jin Feng and
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.,
ISBN 978-0-8218-4145-7,
US $99.00; All AMS Members: US $79.20
Julian D. Cole, On a quasi-linear parabolic equation occurring in aerodynamics, Quart. Appl. Math. 9 (1951), 225–236. MR 42889, DOI 10.1090/S0033-569X-1951-42889-X
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, DOI 10.1007/978-1-4612-5320-4
Jean-Dominique Deuschel and Daniel W. Stroock, Large deviations, Pure and Applied Mathematics, vol. 137, Academic Press, Inc., Boston, MA, 1989. MR 997938
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, DOI 10.1002/9781118165904
W. H. Fleming and P. E. Souganidis, A PDE approach to some large deviations problems, Nonlinear systems of partial differential equations in applied 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
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
Eberhard Hopf, The partial differential equation $u_t+uu_x=\mu u_{xx}$, Comm. Pure Appl. Math. 3 (1950), 201–230. MR 47234, DOI 10.1002/cpa.3160030302
M. Schilder, Some asymptotic formulas for Wiener integrals, Trans. Amer. Math. Soc. 125 (1966), 63–85. MR 201892, DOI 10.1090/S0002-9947-1966-0201892-6
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
V. Strassen, An invariance principle for the law of the iterated logarithm, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 3 (1964), 211–226 (1964). MR 175194, DOI 10.1007/BF00534910
S. R. S. Varadhan, Diffusion processes in a small time interval, Comm. Pure Appl. Math. 20 (1967), 659–685. MR 217881, DOI 10.1002/cpa.3160200404
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, DOI 10.1137/1.9781611970241.bm
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
- Cole, Julian D. On a quasi-linear parabolic equation occurring in aerodynamics, Quart. Appl. Math, 9, 1951, 225–236. MR 0042889 (13:178c)
- Dembo, Amir, Zeitouni, Ofer. Large deviations techniques and applications. Second edition. Applications of Mathematics (New York), 38. Springer-Verlag, New York, 1998. xvi+396 pp. ISBN: 0-387-98406-2. MR 1619036 (99d:60030)
- Deuschel, Jean-Dominique; Stroock, Daniel W. Large deviations. Pure and Applied Mathematics, 137. Academic Press, Inc., Boston, MA, 1989. xiv+307 pp. MR 997938 (90h:60026)
- Dupuis, Paul, Ellis, Richard S. A weak convergence approach to the theory of large deviations. (English summary) Wiley Series in Probability and Statistics: Probability and Statistics. A Wiley-Interscience Publication. John Wiley & Sons, Inc., New York, 1997. xviii+479 pp. ISBN: 0-471-07672-4. MR 1431744 (99f:60057)
- Fleming, W. H., Souganidis, P. E. A PDE approach to some large deviations problems. Nonlinear systems of partial differential equations in applied mathematics, Part 1 (Santa Fe, N.M., 1984), 441–447, Lectures in Appl. Math., 23, Amer. Math. Soc., Providence, RI, 1986. MR 837690 (87i:60032)
- Glass, Michael Steven (1970). Perturbation of a first order equation by a small diffusion. Ph.D. dissertation, New York University, New York, NY. MR 2619818
- Hopf, Eberhard. The partial differential equation $u_t+uu_x=\mu u_{xx}$. Comm. Pure Appl. Math. 3, (1950). 201–230. MR 0047234 (13:846c)
- Schilder, M. Some asymptotic formulas for Wiener integrals. Trans. Amer. Math. Soc. 125 1966 63–85. MR 0201892 (34:1770)
- Shwartz, Adam, Weiss, Alan. Large deviations for performance analysis. Queues, communications, and computing. With an appendix by Robert J. Vanderbei. Stochastic Modeling Series. Chapman & Hall, London, 1995. x+556 pp. ISBN: 0-412-06311-5. MR 1335456 (96i:60029)
- Strassen, V. An invariance principle for the law of the iterated logarithm. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 3 1964 211–226 (1964). MR 0175194 (30:5379)
- Varadhan, S. R. S. Diffusion processes in a small time interval. Comm. Pure Appl. Math. 20 1967 659–685. MR 0217881 (36:970)
- Varadhan, S. R. S. Large deviations and applications. CBMS-NSF Regional Conference Series in Applied Mathematics, 46. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1984. v+75 pp. ISBN: 0-89871-189-4. MR 758258 (86h:60067b)
- Ventcel, A. D., Freidlin, M. I. Small random perturbations of dynamical systems. (Russian) Uspehi Mat. Nauk 25 1970 no. 1 (151), 3–55. 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.
49 (2012), 597-601
DOI:
https://doi.org/10.1090/S0273-0979-2011-01357-X
Published electronically:
October 26, 2011
Review copyright:
© Copyright 2011
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
