Grandes déviations
Séminaire Bourbaki : volume 1986/87, exposés 669-685, Astérisque no. 152-153  (1987), Talk no. 680, p. 207-227
@incollection{SB_1986-1987__29__207_0,
     author = {Sznitman, Alain-Sol},
     title = {Grandes d\'eviations},
     booktitle = {S\'eminaire Bourbaki : volume 1986/87, expos\'es 669-685},
     author = {Collectif},
     series = {Ast\'erisque},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {152-153},
     year = {1987},
     note = {talk:680},
     pages = {207-227},
     zbl = {0636.60023},
     mrnumber = {936856},
     language = {fr},
     url = {http://www.numdam.org/item/SB_1986-1987__29__207_0}
}
Sznitman, Alain-Sol. Grandes déviations, in Séminaire Bourbaki : volume 1986/87, exposés 669-685, Astérisque, no. 152-153 (1987), Talk no. 680, pp. 207-227. http://www.numdam.org/item/SB_1986-1987__29__207_0/

[1] R. Azencott - Grandes déviations et applications, Lect. Notes in Math. 774, Springer (1980). | MR 590626 | Zbl 0435.60028

[2] R. Azencott - Formule de Taylor stochastique..., Lect. Notes in Math. 921, 237-284, Springer (1982). | Numdam | MR 658728 | Zbl 0484.60064

[3] R. Azencott - Densité des diffusions en temps petit..., Lect. Notes in Math. 1059, 402-498, Springer (1984). | Numdam | MR 770974 | Zbl 0546.60079

[4] R. R. Bahadur, S. L. Zabell - Large deviations of the sample mean in general vector space, Ann. Probab. 7, 587-621 (1979). | MR 537209 | Zbl 0424.60028

[5] P. Baldi - Large deviation and stochastic homogeneisation, à paraître Ann. Math. Pura Appl. | Zbl 0654.60024

[6] P. Baldi, M. Chaleyat-Maurel - Sur l'équivalent du module de continuité des diffusions, Séminaire de Probabilités XXI, Lect. Notes in Math., Springer (1987). | Numdam | MR 941996 | Zbl 0617.60034

[7] G. Ben Arous - Développement asymptotique du noyau de la chaleur hors du cutlocus, à paraître. | Numdam | Zbl 0699.35047

[8] J.-M. Bismlt - Large deviations and Malliavin calculus, Progress in Maths. n° 45, Birkhäuser, Basel (1984). | MR 755001 | Zbl 0537.35003

[9] E. Bolthausen - Laplace approximations for sums of independant random vectors, Probab. Th. Rel. Fields, part II (preprint), 72, 2, 305-318 (1986). | MR 836280 | Zbl 0572.60007

[10] F. Comets - Tunnelling and nucleation for a local mean field model, à paraître.

[11] F. Comets - Grandes déviations pour les champs de Gibbs sur Zd , C.R. Acad. Sci., t. 303, série I, n° 11, 511-513 (1986). | MR 865873 | Zbl 0606.60035

[12] H. Cramer - Sur un nouveau théorème limite de la théorie des probabilités, Hermann, Paris (1937). | JFM 64.0529.01

[13] D. A. Dawson, J. Gartner - Long time fluctuations of weakly interacting diffusions, preprint.

[14] M. Donsker, S. R. S. Varadhan - Asymptotic evaluation of certain Wiener integrals for large time, Proc. conf. London, April 1974, A.M. Arthurs Ed., Clarendon, Oxford (1975). | MR 486395 | Zbl 0333.60078

[15] M. Donsker, S. R. S. Varadhan - Asymptotic evaluation of certain Markov process expectations for large time, I, Comm. Pure Appl. Math., 28, 1-47 (1975) ; II, 28, 279-301 (1975) ; III, 29, 389-461 (1977), IV, 36, 183-212 (1983). | MR 386024 | Zbl 0348.60031

[16] M. Donsker, S. R. S. Varadhan - Asymptotics for the Wiener sausage, Comm. Pure Appl. Math., 28, 525-565 (1975). | MR 397901 | Zbl 0333.60077

[17] M. Donsker, S. R. S. Varadhan - On the principal eigenvalue of second-order elliptic differential operator, Comm. Pure Appl. Math., 29, 595-621 (1976). | MR 425380 | Zbl 0356.35065

[18] M. Donsker, S. R. S. Varadhan - On laws of the iterated lagorithm for local times, Comm. Pure Appl. Math., 30, 707-753 (1977). | MR 461682 | Zbl 0356.60029

[19] M. Donsker, S. R. S. Varadhan - On the number of distinct sites visited by a random walk, Comm. Pure Appl. Math., 32, 721-747 (1979). | MR 539157 | Zbl 0418.60074

[20] M. Donsker, S. R. S. Varadhan _ A law of the iterated logarithm for total occupation times of transient Brownian motion, Comm. Pure Appl. Math., 33, 365-393 (1980). | MR 562740 | Zbl 0504.60037

[21] M. Donsker, S. R. S. Varadhan - Asymptotics for the Polaron, Comm. Pure Appl. Math., 36, 505-528 (1983). | MR 709647 | Zbl 0538.60081

[22] M. Donsker, S. R. S. Varadhan - Large deviations for stationary Gaussian processes, Commun. Math. Phys., 97, 187-210 (1985). | MR 782966 | Zbl 0646.60030

[23] H. Doss - Quelques formules asymptotiques pour les perturbations de systèmes dynamiques, Ann. Inst. Henri Poincaré, série B, 16, 1, 17-28 (1980). | Numdam | MR 575173 | Zbl 0432.60073

[24] H. Doss - Démonstration probabiliste de certains développements asymptotiques quasi-classiques, Bull. Sc. Math., 2e série, 109, 179-208 (1985). | MR 802532 | Zbl 0564.35101

[25] M. V. Day - On the asymptotic relation between equilibrium density and exit measure in the exit problem, Stochastics, 12, 303-330 (1984). | MR 749379 | Zbl 0526.60052

[26] R. S. Ellis - Entropy, large deviations and statistical mechanics, Springer, New York (1986). | MR 2189669 | Zbl 0566.60097

[27] R. S. Ellis - Large deviation for the spin per site in Ferromagnetic models, Preprint (1986).

[28] Th. Eisele, R. Lang - Asymptotics for the Wiener sausage with drift, preprint. | MR 863722

[29] W. G. Farris, G. Jona-Lasinio - Large fluctuations for a non-linear heat equation with noise, J. Phys. A : Math. Gen., 15, 3025-3055 (1982). | MR 684578 | Zbl 0496.60060

[30] W. H. Fleming - Exit probabilities and optimal stochastic control, Appl. Math. Optim., 4, 329-346 (1978). | MR 512217 | Zbl 0398.93068

[31] W. H. Fleming - A stochastic control approach to some large deviation problems, Proc. Rome conf., Lect. Notes in Math., 1119, New York (1984). | MR 790689 | Zbl 0585.93067

[32] H. Föllmer, S. Orey - Large deviations for the empirical field of a Gibbs measure, preprint (1986). | MR 942749

[33] M. I. Freidlin - Sublimiting distributions and stabilization of solutions of parabolic equations with a small parameter, Soviet Math. Dokl., 18, 4, 1114-1118 (1977). | MR 454349 | Zbl 0381.35006

[34] M. I. Freidlin - The averaging principle and theorems on large deviations, Russian Math. Surveys, 33, 5, 117-176 (1978). | MR 511884 | Zbl 0416.60029

[35] M. I. Freidlin - Functional integration and partial differential equations, Annals of Math. Studies 109, Princeton Univ. Press, Princeton (1985). | MR 833742 | Zbl 0568.60057

[36] A. Friedman - Stochastic differential equations and applications, Vol. 2, Academic Press, New York (1976). | MR 494491 | Zbl 0323.60057

[37] J. Gartner - On large deviations from the invariant measure, Theory Probab. Appl., 22, 1, 24-39 (1977). | MR 471040 | Zbl 0375.60033

[38] C. J. Holland - A new energy characterization of the smallest eigenvalue of the Schrödinger equation, Comm. Pure Appl. Math., 30, 755-765 (1977). | MR 450768 | Zbl 0358.35060

[39] I. Iscoe, P. Ney, E. Nummelin - Large deviations of uniformly recurrent Markov additive process, Adv. in Appl. Math., 6, 4, 373-412 (1985). | MR 826590 | Zbl 0602.60034

[40] G. Jona-Lasinio, F. Martinelli, E. Scoppola - New approach to the semi-classical limit of quantum mechanics, Commun. Math. Phys., 80, 223-254 (1981). | MR 623159 | Zbl 0483.60094

[41] Y. I. Kifer - On the asymptotics of the transition density of processes with small diffusion, Theory Probab. Appl., 21, 3, 513-522 (1976). | MR 431398 | Zbl 0367.60035

[42] Y. I. Kifer - On the principal eigenvalue in a singular perturbation problem with hyperbolic limit points and circles, J. Diff. Equations, 37, 108-139 (1980). | MR 583343 | Zbl 0413.35010

[43] Y. I. Kifer - The exit problem for small random perturbation of dynamical systems with a hyperbolic fixed point, Israel J. Math. , 40, 1, 74-96 (1981). | MR 636908 | Zbl 0473.60067

[44] S. Kusuoka - The variational principle for stationary Gaussian Markov fields, Lect. Notes in Control 49, 179-187, Springer (1983). | MR 799942 | Zbl 0515.60054

[45] O. E. Lanford - Entropy and Equilibrium states in classical statistical Mechanics, Lect. Notes in Physics, 20, 1-113, Springer (1973).

[46] R. Léandre - Développement asymptotique de la densité des diffusions dégénérées, preprint.

[47] P. L. Lions - Grandes déviations, calcul des variations et solutions de viscosité, preprint.

[48] S. A. Molcanov - Diffusion processes and Riemannian geometry, Russian Math. Survey, 30, 1-53 (1975). | MR 413289 | Zbl 0315.53026

[49] H. Okura - On the spectral distribution of certain integro-differential operators with random potential, Osaka, J. Math., 16, 633-666 (1979). | MR 551581 | Zbl 0435.60066

[50] S. Olla - Large deviations for Gibbs random fields, preprint (1986). | MR 931502

[51] S. Orey - Large deviation in ergodic theory, Sem. on Stoch. Proc. 84, Cinlar Ed. Birkhäuser, Boston (1986). | MR 896730 | Zbl 0585.60039

[52] L. A. Pastur - Behaviour of some Wiener integrals as t → ∞ and the density of states ..., Teor. Mat. Fiz, 32, 88-95 (1977) (en Russe). | Zbl 0353.60053

[53] M. Pincus - Gaussian Processes and Hammerstein integral equations, Trans. Amer. Math. Soc., 134, 193-216 (1968). | MR 231439 | Zbl 0175.12502

[54] P. Priouret - Remarques sur les petites perturbations de systèmes dynamiques, Lect. Notes in Math., 921, 184-200, Springer (1982). | Numdam | MR 658679 | Zbl 0484.60021

[55] T. Rockafellar - Convex Analysis, Princeton University Press, Princeton (1980). | Zbl 0193.18401

[56] I. Sanov - On the probability of large deviations of random variables, Selected Trans. Math. Stat. Prob., 1, 213-244 (1961). | MR 116378 | Zbl 0112.10106

[57] Séminaire Orsay - Grandes déviations et applications statistiques, Astérisque 68, S.M.F., Paris (1979). | Numdam | MR 568892 | Zbl 0408.00011

[58] M. Schilder - Some asymptotic formulae for Wiener integrals, Trans. Amer. Math. Soc., 125, 63-85 (1966). | MR 201892 | Zbl 0156.37602

[59] D. W. Stroock - An introduction to the theory of large deviations, Springer, New York (1984). | MR 755154 | Zbl 0552.60022

[60] Y. Takahashi - Entropy function for dynamical systems and their random perturbation, Proc. Int. Symp. on S.D.E., Kyoto (1982).

[61] S. R. S. Varadhan - Asymptotic probabilities and differential equations, Comn. Pure Appl. Math., 19, 261-296 (1966). | MR 203230 | Zbl 0147.15503

[62] S. R. S. Varadhan - Diffusion processes in a small time interval, Comm. Pure Appl. Math., 20, 659-685 (1967). | MR 217881 | Zbl 0278.60051

[63] S. R. S. Varadhan - Large deviations and applications, SIAM, Philadelphia (1984). | MR 758258

[64] A. D. Ventsel - On the asymptotics of matrices with elements..., Soviet Math. Dokl., 13, 1, 65-68 (1972). | Zbl 0291.15018

[65] A. D. Ventsel - Formulae for eigenfunctions and eigenmeasures associated with a Markov process, Theory Probab. Appl., 18, 1, 1-26 (1973). | Zbl 0287.60067

[66] A. D. Ventsel, M. I. Freidlin - On small random perturbations of dynamical systems, Russian Math. Surveys, 25, 1, 1-55 (1970). | MR 267221 | Zbl 0297.34053

[67] A. D. Ventsel, M. I. Freidlin - Random perturbations of dynamical systems, Springer, New York (1984). | MR 722136 | Zbl 0522.60055

[68] M. I. Freidlin - Limit theorems for large deviations and reaction-diffusion equations, Ann. Prob., 13, 3, 639-675 (1985). | MR 799415 | Zbl 0576.60070

[69] M. Cassandro, E. Olivieri, P. Picco - Small random perturbations of infinite dimensional dynamical systems and nucleation theory, Ann. Inst. H. Poincaré, Phys. th., 44, 4, 343-396 (1986). | Numdam | MR 850897 | Zbl 0598.35133