Grandes déviations

Alain-Sol Sznitman

Séminaire Bourbaki (1986-1987)

  • Volume: 29, page 207-227
  • ISSN: 0303-1179

How to cite

top

Sznitman, Alain-Sol. "Grandes déviations." Séminaire Bourbaki 29 (1986-1987): 207-227. <http://eudml.org/doc/110080>.

@article{Sznitman1986-1987,
author = {Sznitman, Alain-Sol},
journal = {Séminaire Bourbaki},
keywords = {Random perturbations of dynamical systems; Sanov's problem; occupation times; large deviations for Gibbs fields},
language = {fre},
pages = {207-227},
publisher = {Société Mathématique de France},
title = {Grandes déviations},
url = {http://eudml.org/doc/110080},
volume = {29},
year = {1986-1987},
}

TY - JOUR
AU - Sznitman, Alain-Sol
TI - Grandes déviations
JO - Séminaire Bourbaki
PY - 1986-1987
PB - Société Mathématique de France
VL - 29
SP - 207
EP - 227
LA - fre
KW - Random perturbations of dynamical systems; Sanov's problem; occupation times; large deviations for Gibbs fields
UR - http://eudml.org/doc/110080
ER -

References

top
  1. [1] R. Azencott - Grandes déviations et applications, Lect. Notes in Math.774, Springer (1980). Zbl0435.60028MR590626
  2. [2] R. Azencott - Formule de Taylor stochastique..., Lect. Notes in Math.921, 237-284, Springer (1982). Zbl0484.60064MR658728
  3. [3] R. Azencott - Densité des diffusions en temps petit..., Lect. Notes in Math.1059, 402-498, Springer (1984). Zbl0546.60079MR770974
  4. [4] R.R. Bahadur, S.L. Zabell - Large deviations of the sample mean in general vector space, Ann. Probab.7, 587-621 (1979). Zbl0424.60028MR537209
  5. [5] P. Baldi - Large deviation and stochastic homogeneisation, à paraître Ann. Math. Pura Appl. Zbl0654.60024
  6. [6] P. Baldi, M. Chaleyat-Maurel - Sur l'équivalent du module de continuité des diffusions, Séminaire de ProbabilitésXXI, Lect. Notes in Math., Springer (1987). Zbl0617.60034MR941996
  7. [7] G. Ben Arous - Développement asymptotique du noyau de la chaleur hors du cutlocus, à paraître. Zbl0699.35047
  8. [8] J.-M. Bismlt - Large deviations and Malliavin calculus, Progress in Maths. n° 45, Birkhäuser, Basel (1984). Zbl0537.35003MR755001
  9. [9] E. Bolthausen - Laplace approximations for sums of independant random vectors, Probab. Th. Rel. Fields, part II (preprint), 72, 2, 305-318 (1986). Zbl0572.60007MR836280
  10. [10] F. Comets - Tunnelling and nucleation for a local mean field model, à paraître. 
  11. [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). Zbl0606.60035MR865873
  12. [12] H. Cramer - Sur un nouveau théorème limite de la théorie des probabilités, Hermann, Paris (1937). JFM64.0529.01
  13. [13] D.A. Dawson, J. Gartner - Long time fluctuations of weakly interacting diffusions, preprint. 
  14. [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). Zbl0333.60078MR486395
  15. [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). Zbl0348.60031
  16. [16] M. Donsker, S.R.S. Varadhan - Asymptotics for the Wiener sausage, Comm. Pure Appl. Math., 28, 525-565 (1975). Zbl0333.60077MR397901
  17. [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). Zbl0356.35065MR425380
  18. [18] M. Donsker, S.R.S. Varadhan - On laws of the iterated lagorithm for local times, Comm. Pure Appl. Math., 30, 707-753 (1977). Zbl0356.60029MR461682
  19. [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). Zbl0418.60074MR539157
  20. [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). Zbl0504.60037MR562740
  21. [21] M. Donsker, S.R.S. Varadhan - Asymptotics for the Polaron, Comm. Pure Appl. Math., 36, 505-528 (1983). Zbl0538.60081MR709647
  22. [22] M. Donsker, S.R.S. Varadhan - Large deviations for stationary Gaussian processes, Commun. Math. Phys., 97, 187-210 (1985). Zbl0646.60030MR782966
  23. [23] H. Doss - Quelques formules asymptotiques pour les perturbations de systèmes dynamiques, Ann. Inst. Henri Poincaré, série B, 16, 1, 17-28 (1980). Zbl0432.60073MR575173
  24. [24] H. Doss - Démonstration probabiliste de certains développements asymptotiques quasi-classiques, Bull. Sc. Math., 2e série, 109, 179-208 (1985). Zbl0564.35101MR802532
  25. [25] M.V. Day - On the asymptotic relation between equilibrium density and exit measure in the exit problem, Stochastics, 12, 303-330 (1984). Zbl0526.60052MR749379
  26. [26] R.S. Ellis - Entropy, large deviations and statistical mechanics, Springer, New York (1986). Zbl0566.60097MR2189669
  27. [27] R.S. Ellis - Large deviation for the spin per site in Ferromagnetic models, Preprint (1986). 
  28. [28] Th. Eisele, R. Lang - Asymptotics for the Wiener sausage with drift, preprint. MR863722
  29. [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). Zbl0496.60060MR684578
  30. [30] W.H. Fleming - Exit probabilities and optimal stochastic control, Appl. Math. Optim., 4, 329-346 (1978). Zbl0398.93068MR512217
  31. [31] W.H. Fleming - A stochastic control approach to some large deviation problems, Proc. Rome conf., Lect. Notes in Math., 1119, New York (1984). Zbl0585.93067MR790689
  32. [32] H. Föllmer, S. Orey - Large deviations for the empirical field of a Gibbs measure, preprint (1986). MR942749
  33. [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). Zbl0381.35006MR454349
  34. [34] M.I. Freidlin - The averaging principle and theorems on large deviations, Russian Math. Surveys, 33, 5, 117-176 (1978). Zbl0416.60029MR511884
  35. [35] M.I. Freidlin - Functional integration and partial differential equations, Annals of Math. Studies 109, Princeton Univ. Press, Princeton (1985). Zbl0568.60057MR833742
  36. [36] A. Friedman - Stochastic differential equations and applications, Vol. 2, Academic Press, New York (1976). Zbl0323.60057MR494491
  37. [37] J. Gartner - On large deviations from the invariant measure, Theory Probab. Appl., 22, 1, 24-39 (1977). Zbl0375.60033MR471040
  38. [38] C.J. Holland - A new energy characterization of the smallest eigenvalue of the Schrödinger equation, Comm. Pure Appl. Math., 30, 755-765 (1977). Zbl0358.35060MR450768
  39. [39] I. Iscoe, P. Ney, E. Nummelin - Large deviations of uniformly recurrent Markov additive process, Adv. in Appl. Math., 6, 4, 373-412 (1985). Zbl0602.60034MR826590
  40. [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). Zbl0483.60094MR623159
  41. [41] Y.I. Kifer - On the asymptotics of the transition density of processes with small diffusion, Theory Probab. Appl., 21, 3, 513-522 (1976). Zbl0367.60035MR431398
  42. [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). Zbl0413.35010MR583343
  43. [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). Zbl0473.60067MR636908
  44. [44] S. Kusuoka - The variational principle for stationary Gaussian Markov fields, Lect. Notes in Control49, 179-187, Springer (1983). Zbl0515.60054MR799942
  45. [45] O.E. Lanford - Entropy and Equilibrium states in classical statistical Mechanics, Lect. Notes in Physics, 20, 1-113, Springer (1973). 
  46. [46] R. Léandre - Développement asymptotique de la densité des diffusions dégénérées, preprint. 
  47. [47] P.L. Lions - Grandes déviations, calcul des variations et solutions de viscosité, preprint. 
  48. [48] S.A. Molcanov - Diffusion processes and Riemannian geometry, Russian Math. Survey, 30, 1-53 (1975). Zbl0315.53026MR413289
  49. [49] H. Okura - On the spectral distribution of certain integro-differential operators with random potential, Osaka, J. Math., 16, 633-666 (1979). Zbl0435.60066MR551581
  50. [50] S. Olla - Large deviations for Gibbs random fields, preprint (1986). MR931502
  51. [51] S. Orey - Large deviation in ergodic theory, Sem. on Stoch. Proc.84, Cinlar Ed. Birkhäuser, Boston (1986). Zbl0585.60039MR896730
  52. [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). Zbl0353.60053
  53. [53] M. Pincus - Gaussian Processes and Hammerstein integral equations, Trans. Amer. Math. Soc., 134, 193-216 (1968). Zbl0175.12502MR231439
  54. [54] P. Priouret - Remarques sur les petites perturbations de systèmes dynamiques, Lect. Notes in Math., 921, 184-200, Springer (1982). Zbl0484.60021MR658679
  55. [55] T. Rockafellar - Convex Analysis, Princeton University Press, Princeton (1980). Zbl0193.18401
  56. [56] I. Sanov - On the probability of large deviations of random variables, Selected Trans. Math. Stat. Prob., 1, 213-244 (1961). Zbl0112.10106MR116378
  57. [57] Séminaire Orsay - Grandes déviations et applications statistiques, Astérisque68, S.M.F., Paris (1979). Zbl0408.00011MR568892
  58. [58] M. Schilder - Some asymptotic formulae for Wiener integrals, Trans. Amer. Math. Soc., 125, 63-85 (1966). Zbl0156.37602MR201892
  59. [59] D.W. Stroock - An introduction to the theory of large deviations, Springer, New York (1984). Zbl0552.60022MR755154
  60. [60] Y. Takahashi - Entropy function for dynamical systems and their random perturbation, Proc. Int. Symp. on S.D.E., Kyoto (1982). 
  61. [61] S.R.S. Varadhan - Asymptotic probabilities and differential equations, Comn. Pure Appl. Math., 19, 261-296 (1966). Zbl0147.15503MR203230
  62. [62] S.R.S. Varadhan - Diffusion processes in a small time interval, Comm. Pure Appl. Math., 20, 659-685 (1967). Zbl0278.60051MR217881
  63. [63] S.R.S. Varadhan - Large deviations and applications, SIAM, Philadelphia (1984). MR758258
  64. [64] A.D. Ventsel - On the asymptotics of matrices with elements..., Soviet Math. Dokl., 13, 1, 65-68 (1972). Zbl0291.15018
  65. [65] A.D. Ventsel - Formulae for eigenfunctions and eigenmeasures associated with a Markov process, Theory Probab. Appl., 18, 1, 1-26 (1973). Zbl0287.60067
  66. [66] A.D. Ventsel, M.I. Freidlin - On small random perturbations of dynamical systems, Russian Math. Surveys, 25, 1, 1-55 (1970). Zbl0297.34053MR267221
  67. [67] A.D. Ventsel, M.I. Freidlin - Random perturbations of dynamical systems, Springer, New York (1984). Zbl0522.60055MR722136
  68. [68] M.I. Freidlin - Limit theorems for large deviations and reaction-diffusion equations, Ann. Prob., 13, 3, 639-675 (1985). Zbl0576.60070MR799415
  69. [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). Zbl0598.35133MR850897

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.