The Annals of Probability

Large deviations

S. R. S. Varadhan

Source: Ann. Probab. Volume 36, Number 2 (2008), 397-419.

Abstract

This paper is based on Wald Lectures given at the annual meeting of the IMS in Minneapolis during August 2005. It is a survey of the theory of large deviations.

Primary Subjects: 60-02, 60F10
Keywords: Large deviations; rare events

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Permanent link to this document: http://projecteuclid.org/euclid.aop/1204306957
Digital Object Identifier: doi:10.1214/07-AOP348
Mathematical Reviews number (MathSciNet): MR2393987

References

Cramèr, H. (1938). Sur un nouveau théorème-limite de la théorie des probabilités. Actualités Scientifiques et Industrialles 736 5–23. Colloque Consecré à la Théorie des Probabilités 3. Hermann, Paris.
Dembo, A. and Zeitouni, O. (1998). Large Deviations Techniques and Applications, 2nd ed. Springer, New York.
Mathematical Reviews (MathSciNet): MR1619036
Zentralblatt MATH: 0896.60013
Donsker, M. D. and Varadhan, S. R. S. (1975). Asymptotic evaluation of certain Markov process expectations for large time. I. Comm. Pure Appl. Math. 28 1–47.
Donsker, M. D. and Varadhan, S. R. S. (1975). Asymptotic evaluation of certain Markov process expectations for large time. II. Comm. Pure Appl. Math. 28 279–301.
Donsker, M. D. and Varadhan, S. R. S. (1976). Asymptotic evaluation of certain Markov process expectations for large time. III. Comm. Pure Appl. Math. 29 389–461.
Mathematical Reviews (MathSciNet): MR428471
Digital Object Identifier: doi:10.1002/cpa.3160290405
Donsker, M. D. and Varadhan, S. R. S. (1983). Asymptotic evaluation of certain Markov process expectations for large time. IV. Comm. Pure Appl. Math. 36 183–212.
Mathematical Reviews (MathSciNet): MR690656
Digital Object Identifier: doi:10.1002/cpa.3160360204
Deuschel, J. D. and Stroock, D. W. (1989). Large Deviations. Academic Press, Boston.
Mathematical Reviews (MathSciNet): MR997938
Dupuis, P. and Ellis, R. S. (1997). A Weak Convergence Approach to the Theory of Large Deviations. Wiley, New York.
Mathematical Reviews (MathSciNet): MR1431744
Zentralblatt MATH: 0904.60001
Ellis, R. S. (2006). Entropy, Large Deviations, and Statistical Mechanics. Springer, Berlin.
Mathematical Reviews (MathSciNet): MR2189669
Zentralblatt MATH: 05014859
Esscher, F. (1932). On the probability function in the collective theory of risk. Skandinavisk Aktuarietidskrift 15 175–195.
Feng, J. and Kurtz, T. G. (2006). Large Deviations for Stochastic Processes. Amer. Math. Soc., Providence, RI.
Mathematical Reviews (MathSciNet): MR2260560
Freidlin, M. I. and Wentzell, A. D. (1998). Random Perturbations of Dynamical Systems, 2nd ed. Springer, New York.
Mathematical Reviews (MathSciNet): MR1652127
Zentralblatt MATH: 0922.60006
Gärtner, J. (1977). On large deviations from an invariant measure (in Russian). Teor. Verojatnost. i Primenen. 22 27–42.
Mathematical Reviews (MathSciNet): MR471040
Kipnis, C. and Landim, C. (1999). Scaling Limits of Interacting Particle Systems. Springer, Berlin.
Mathematical Reviews (MathSciNet): MR1707314
Zentralblatt MATH: 0927.60002
Kosygina, E., Rezakhanlou, F. and Varadhan, S. R. S. (2006). Stochastic homogenization of Hamilton–Jacobi–Bellman equations. Comm. Pure Appl. Math. 59 1489–1521.
Mathematical Reviews (MathSciNet): MR2248897
Digital Object Identifier: doi:10.1002/cpa.20137
Lanford, O. E. (1973). Entropy and equilibrium states in classical statistical mechanics. In Statistical Mechanics and Mathematical Problems (A. Lenard, ed.) 1–113. Lecture Notes in Phys. 20. Springer, Berlin.
Lions, P. L. and Souganidis, P. E. (2005). Homogenization of “viscous” Hamilton–Jacobi equations in stationary ergodic media. Comm. Partial Differential Equations 30 335–375.
Mathematical Reviews (MathSciNet): MR2131058
Digital Object Identifier: doi:10.1081/PDE-200050077
Sanov, I. N. (1957). On the probability of large deviations of random magnitudes (in Russian). Mat. Sb. N. S. 42 (84) 11–44.
Mathematical Reviews (MathSciNet): MR88087
Shwartz, A. and Weiss, A. (1995). Large Deviations for Performance Analysis. Chapman and Hall, London.
Mathematical Reviews (MathSciNet): MR1335456
Varadhan, S. R. S. (1967). Diffusion processes in a small time interval. Comm. Pure Appl. Math. 20 659–685.
Mathematical Reviews (MathSciNet): MR217881
Digital Object Identifier: doi:10.1002/cpa.3160200404
Varadhan, S. R. S. (1984). Large Deviations and Applications. SIAM, Philadelphia.
Mathematical Reviews (MathSciNet): MR758258
Zentralblatt MATH: 0549.60023
Varadhan, S. R. S. (2003). Large deviations and entropy. In Entropy. Princeton Ser. Appl. Math. 199–214. Princeton Univ. Press.
Mathematical Reviews (MathSciNet): MR2035822
Zentralblatt MATH: 02026092
Varadhan, S. R. S. (1996). The complex story of simple exclusion. In Itô’s Stochastic Calculus and Probability Theory 385–400. Springer, Tokyo.
Mathematical Reviews (MathSciNet): MR1439538
Zentralblatt MATH: 0866.60092
Varadhan, S. R. S. (2003). Large deviations for random walks in a random environment. Dedicated to the memory of Jürgen K. Moser. Comm. Pure Appl. Math. 56 1222–1245.
Zeitouni, O. (2002). Random walks in random environments. In Proceedings of the International Congress of Mathematicians III (Beijing, 2002) 117–127. Higher Ed. Press, Beijing.
Mathematical Reviews (MathSciNet): MR1957524
Zentralblatt MATH: 1007.60102

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