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Grandes deviations et applications

  • R. Azencott
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 774)

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Bibliographie

  1. [1]
    R. AZENCOTT-Methods of localisation and diffusions on manifolds (à paraître)Google Scholar
  2. [2]
    R. AZENCOTT-Behaviour of diffusion semi-groups at infinity. Bull. Soc. Math. France 102, 1974, p. 193–240MathSciNetzbMATHGoogle Scholar
  3. [3]
    R. AZENCOTT-G. RUGET-Mélanges d’équations différentielles et grands écarts à la loi des grands nombres. Z. Wahrscheinlichkeit. verw. Gebiete 38, 1977, p. 1–54MathSciNetCrossRefzbMATHGoogle Scholar
  4. [4]
    A. BADRIKIAN-Fonctions aléatoires linéaires et mesures cylindriques. Lecture Notes Math. 139 (1970)Google Scholar
  5. [5]
    R.R. BAHADUR-Rates of convergence of estimates and test statistics Ann. Math. Stat. 38 (1967) p. 303–324MathSciNetCrossRefzbMATHGoogle Scholar
  6. [6]
    R.R. BAHADUR-Some limit theorems in statistics. SIAM (1971) PhiladelphiaGoogle Scholar
  7. [7]
    R.R. BAHADUR-S.L. ZABELL-Large deviations of the sample mean in general vector spaces (à paraître)Google Scholar
  8. [8]
    P. BILLINGSLEY-Ergodic theory and information. Wiley-New-York (1965)zbMATHGoogle Scholar
  9. [9]
    J.M. BONY-Cours au C.I.M.E. (1969)Google Scholar
  10. [10]
    H. CHERNOFF-Asymptotic efficiency for tests based on the sum of observations. Ann. Math. Stat. 23 (1952), p. 493–507MathSciNetCrossRefzbMATHGoogle Scholar
  11. [11]
    J. CHRISTENSEN-Topology and borel structures. North Holland Amsterdam (1974)zbMATHGoogle Scholar
  12. [12]
    COURANT-HILBERT-Methods of Mathematical Physics. Interscience (1962)Google Scholar
  13. [13]
    P. COURREGE-P. PRIOURET-Recollement de processus de Markov. Pub. Inst. Stat. Univ. Paris 14 (1965) p. 275–325MathSciNetzbMATHGoogle Scholar
  14. [14]
    H. CRAMER-Sur un nouveau théorème limite de la théorie des probabilités. Colloquium on theory of probability. Paris-Hermann (1937)Google Scholar
  15. [15]
    M. DONSKER-S. VARADHAN-Asymptotic evaluation of certain Markov processes expectations for large time. I, II, III Comm. Pure App. Math. 28 (1975) p. 1–47 29 (1976) p. 279–301 29 (1976) p. 389–461MathSciNetCrossRefzbMATHGoogle Scholar
  16. [16]
    M. DONSKER-S. VARADHAN-Large deviations for Markov processes and asymptotic evaluation of certain expectations for large time in "Probabilistic methods in differential equations". Lecture Notes in Math., Springer, 451 (1975) p. 82–87Google Scholar
  17. [17]
    H. DOSS-Quelques formules asymptotiques pour les petites perturbations de systèmes dynamiques (à paraître)Google Scholar
  18. [18]
    E. DYNKIN-Markov processes I, II. SpringerGoogle Scholar
  19. [19]
    N. EL KAROUI-Thèse Université PARIS VIGoogle Scholar
  20. [20]
    W. FELLER-Limit theorems for probabilities of large deviations. Z. Wahrscheinlich. verw. Geb. 14 (1969) p. 1–20MathSciNetCrossRefzbMATHGoogle Scholar
  21. [21]
    W. FELLER-Generalisation of a theorem of Cramer. Trans. Am. Math. Soc. 54 (1943) p. 361–372MathSciNetzbMATHGoogle Scholar
  22. [22]
    X. FERNIQUE-Régularité des trajectoires des fonctions aléatoires gaussiennes. Ecole d’Eté Saint-Flour IV (1975). Lecture Notes Math. 480Google Scholar
  23. [23]
    M.I. FREIDLIN-Action functional for a class of stochastic processes Th. Prob. App. 17 (1972) p. 511–515CrossRefzbMATHGoogle Scholar
  24. [24]
    B. GAVEAU-Principe de moindre action. Propagation de la chaleur. Estimées sous elliptiques sur certains groupes nilpotents. Acta Math. 139 (1977) p. 96–153MathSciNetCrossRefGoogle Scholar
  25. [25]
    B. GAVEAU-Systèmes hamiltoniens associés à certains opérateurs hypoelliptiques. Bull. Sci. Math. (1978)Google Scholar
  26. [26]
    S. HELGASON-Differential geometry and symmetric spaces. Academic Press. New-York (1962)zbMATHGoogle Scholar
  27. [27]
    N. KRYLOV-Control of a solution of a stochastic integral equations. Th. Prob. App. 17 (1972) p. 114–131CrossRefzbMATHGoogle Scholar
  28. [28]
    KULLBACK-Information theoryGoogle Scholar
  29. [29]
    H. KUO-Gaussian measures in Banach spaces. Lecture Notes in Math. 526 (1975)Google Scholar
  30. [30]
    O. LANFORD-Entropy and equilibrium states in classical statistical mechanics. Lecture Notes Physics 20 (1971) p. 1–113CrossRefGoogle Scholar
  31. [31]
    Y. LINNIK-Large deviations for the sum of independent variables. Proc. 4th-Berkeley Symp. 2 (1961) p. 289–306MathSciNetGoogle Scholar
  32. [32]
    P.L. LIONS-Résolution des problèmes généraux de Bellman-Dirichlet C.R. Acad. Sci. Paris 287 (1978) p. 747–750zbMATHGoogle Scholar
  33. [33]
    P.L. LIONS-Contrôle de diffusions dans Rn. C.R. Acad. Sci. Paris (à paraître)Google Scholar
  34. [34]
    D. MANANKIANDRIANANA-Noyau de la chaleur d’un opérateur hypoelliptique dégénéré (comportement pour des temps petits). C.R. Acad. Sci. Paris (à paraître)Google Scholar
  35. [35]
    P.A. MEYER-Probabilités et Potentiel-Hermann-Paris (1966)Google Scholar
  36. [36]
    J. MILNOR-Morse theory-Ann. Math. Studies 51. Princeton (1963)Google Scholar
  37. [37]
    S. MOLCHANOV-Diffusions et géométrie riemannienne. Uspetchi Mat. Nayk. 30 (1975) p. 3–59Google Scholar
  38. [38]
    A. NAGAEV-Integral limit theorems taking large deviations into account when Cramer’s conditions does not hold I, II Th. Prob. Appl. 14 (1969) p. 51–64, p. 193–208MathSciNetCrossRefzbMATHGoogle Scholar
  39. [39]
    V. PETROV-Sums of independent random variables. Springer-Verlag New-York (1975)CrossRefzbMATHGoogle Scholar
  40. [40]
    P. PRIOURET-Diffusions et équations différentielles stochastiques. in "Ecole d’Eté Saint Flour III-1973". Lecture Notes in Math. Springer-Verlag 390 (1974)Google Scholar
  41. [41]
    R. ROCKAFELLAR-Measurable dependence of convex sets on parameters. J Math. Ana. App. 28 (1969) p. 4–25MathSciNetCrossRefzbMATHGoogle Scholar
  42. [42]
    R. ROCKAFELLAR-Convex analysis-Princeton University Press. Princeton (1970)CrossRefzbMATHGoogle Scholar
  43. [43]
    I. SANOV-On the probability of large deviations of random variable Selected Trans. Math. Stat. Prob. 1 (1961) p. 213–244MathSciNetzbMATHGoogle Scholar
  44. [44]
    M. SCHILDER-Asymptotic formulas for Wiener integrals. Trans. Am. Math. Soc. 125 (1966) p. 63–85MathSciNetCrossRefzbMATHGoogle Scholar
  45. [45]
    L. SCHWARTZ-Semi martingales sur des variétés. Martingales conformes sur des variétés analytiques complexes. Cours Ecole Polytechnique (1978) (à paraître)Google Scholar
  46. [46]
    Séminaire de Probabilités, Paris VII (1977–79) (à paraître)Google Scholar
  47. [47]
    Séminaire de Statistiques, Orsay 1977–78 (à paraître)Google Scholar
  48. [48]
    A.V. SKOROKHOD-Note on Gaussian measures in a Banach space Th. Prob. Appl. 15 (1970) p. 508MathSciNetCrossRefzbMATHGoogle Scholar
  49. [49]
    D. STROOCK-S.R. VARADHAN-Diffusion processes with continuous coefficients. Comm. Pure App. Math. 22 (1969) p. 345–400 et p. 479–530MathSciNetCrossRefzbMATHGoogle Scholar
  50. [50]
    S. VARADHAN-Asymptotic probabilities and differential equations Comm. Pure App. Math 1 (1966), p. 261–286MathSciNetCrossRefzbMATHGoogle Scholar
  51. [51]
    A.D. VENTSEL-Rough limit theorems on large deviations for Markov processes I, II. Th. Prob. Appl. 21 (1976) p. 227–242 et p. 499–512MathSciNetCrossRefGoogle Scholar
  52. [52]
    A.D. VENTSEL-Action functional for gaussian random functions. Th. Prob. Appl. 17 (1972) p. 515–517CrossRefGoogle Scholar
  53. [53]
    A.D. VENTSEL-M.I. FREIDLIN-On small random perturbations of dynamical systems. Russian Math. Surveys 25 (1970) p. 1–55MathSciNetCrossRefzbMATHGoogle Scholar
  54. [54]
    A.D. VENTSEL-M.I. FREIDLIN-Some problems concerning stability under small random perturbations. Th. Prob. App. 17 (1972) p. 269–283CrossRefzbMATHGoogle Scholar

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© Springer-Verlag 1980

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  • R. Azencott

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