Classes uniformes de processus gaussiens stationnaires

  • Michel Weber
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 581)


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Yu. K. BELYAEV [1961], "Continuity and Hölder conditions for sample functions of stationary Gaussian processes", Proc. 4 th. Berkeley Symp. on Math. Stat. and Prob. 2, pp. 23–33.MathSciNetGoogle Scholar
  2. [2]
    S.M. BERMAN [1962], "A law of large numbers for the maximum in a stationary Gaussian sequence", Ann. Math. Statist. 33, pp. 93.97.MathSciNetGoogle Scholar
  3. [3]
    S.M. BERMAN [1970], "Gaussian processes with stationary increments: local times and sample functions properties", Ann. Math. Statist. 41 pp. 1260–1272.MathSciNetCrossRefzbMATHGoogle Scholar
  4. [4]
    Z. CIESIELSKI [1961], "Hölder conditions for realizations of Gaussian processes", Trans. Amer. Math. Soc. 99 pp. 403–413.MathSciNetzbMATHGoogle Scholar
  5. [5]
    R.M. DUDLEY [1967], "The sizes of compact subsets of Hilbert space and continuity of Gaussian processes", J. Functional Analysis 1, pp. 290–330.MathSciNetCrossRefzbMATHGoogle Scholar
  6. [6]
    X. FERNIQUE [1964], "Continuité des processus gaussiens", C.R Acad. Scienc. Paris 258, pp. 6058–6060.MathSciNetzbMATHGoogle Scholar
  7. [7]
    X. FERNIQUE [1970], "Intégrabilité des vecteurs gaussiens", C.R. Acad. Scienc. Paris 270 Sér. A pp. 1698–1699.MathSciNetzbMATHGoogle Scholar
  8. [8]
    X. FERNIQUE [1975], "Régularité des trajectoires des fonctions aléatoires gaussiennes, Lectures Notes Springer.Google Scholar
  9. [9]
    A. GARSIA, E. RODEMICH and H. RUMSEY Jr. [1970], "A real variable lemma and the continuity of paths of some Gaussian processes", Indiana Univ. Math. J. 20 pp. 565–578.MathSciNetCrossRefzbMATHGoogle Scholar
  10. [10]
    G.A. HUNT [1951], "Random Fourier transforms", Trans. Amer. Math. Soc. 71, pp. 38–69.MathSciNetCrossRefzbMATHGoogle Scholar
  11. [11]
    K. ITÔ and M. NISIO [1968], "On the oscillation functions of Gaussian processes", Math. Scand. 22, pp. 209–223.MathSciNetCrossRefzbMATHGoogle Scholar
  12. [12]
    N.C. JAIN and G. KALLIANPUR [1970], "Norm convergent expansions for Gaussian processes in Banach spaces", Proc. Amer. Math. Soc. 25, pp. 890–895.MathSciNetzbMATHGoogle Scholar
  13. [13]
    J.P. KAHANE [1960], "Propriétés locales des fonctions à séries de Fourier aléatoires", Studia Math. 19, pp. 1–25.MathSciNetzbMATHGoogle Scholar
  14. [14]
    J. KARAMATA [1933], "Sur un mode de croissance réguliēre — théorēmes fondamentaux". Bulletin de la Soc. Math. de France 61, pp. 55–62.MathSciNetzbMATHGoogle Scholar
  15. [15]
    T. KAWADA [1969], "On the upper and lower class for Gaussian processes with several parameter", Nagoya Math. J. Vol. 35, pp. 109–132.MathSciNetCrossRefzbMATHGoogle Scholar
  16. [16]
    N. KÔNO [1970], "On the modulus of continuity of sample functions of Gaussian processes", J. Math. Kyoto Univ. 10, pp. 493–536.MathSciNetzbMATHGoogle Scholar
  17. [17]
    N. KÔNO [1975], "Asymptotic Behaviour of Sample Functions of Gaussian Random Fields", (à paraître dans J. Math. Kyota Univ.).Google Scholar
  18. [18]
    P. LEVY [1937], "Théorie de l'addition des variables aléatoires", (Paris, Gauthier-Villars).zbMATHGoogle Scholar
  19. [19]
    P. LEVY [1965], "Processus stochastiques et mouvement brownien", (Paris, Gauthier-Villars).zbMATHGoogle Scholar
  20. [20]
    M.B. MARCUS [1968], "Hölder conditions for Gaussian processes with stationary increments", Trans. Amer. Math. Soc. 134, pp. 29–52.MathSciNetzbMATHGoogle Scholar
  21. [21]
    M.B. MARCUS [1970], "Hölder conditions for continuous Gaussian processes" Osuka J. Math. 7, pp. 483–494.zbMATHGoogle Scholar
  22. [22]
    M.B. MARCUS [1971], Gaussian lacunary series and the modulus of continuity for Gaussian processes.Google Scholar
  23. [23]
    M.B. MARCUS and L.A. SCHEPP [1970], "Continuity of Gaussian processes", Trans. Amer. Math. Soc. 151, pp. 377–392.MathSciNetCrossRefGoogle Scholar
  24. [24]
    I. PETROWSKI [1935], "Zur ersten Randwertaufgabe der Wärmeleitungleichung", Compositio Math. 1, pp. 383–419.MathSciNetGoogle Scholar
  25. [25]
    J. PICKANDS [1967], "Maxima of stationary Gaussian processes", Z. Wahrscheinlichkeitsth. 7, pp. 190–223.MathSciNetCrossRefzbMATHGoogle Scholar
  26. [26]
    C. PRESTON [1972], "Continuity properties of some Gaussian processes", Amer. Math. Statist. 43 pp. 285–292.MathSciNetCrossRefzbMATHGoogle Scholar
  27. [27]
    T. SIRAO [1960], "On the continuity of Brownian motion with a multidimensional parameter", Nagoya Math. J. 16, pp. 135–136.MathSciNetCrossRefzbMATHGoogle Scholar
  28. [28]
    T. Sirao and H. Watanabé [1970], "On the upper and lower class of stationary Gaussian processes", Trans. Amer. Math. Soc. 147, pp. 301–331.MathSciNetCrossRefzbMATHGoogle Scholar
  29. [29]
    T. SIRAO, K.L. CHUNG and P. ERDÖS [1959], "On the Lipschitz's condition for Brownian Motion", J. Math. Soc. Japan Vol. 11, no 4, pp. 263–274.MathSciNetCrossRefzbMATHGoogle Scholar
  30. [30]
    D. SLEPIAN [1962], "The one-sided barrier problem for Gaussian noise", Bell. syst. tech. Jour. 41, pp. 463–501.MathSciNetCrossRefGoogle Scholar
  31. [31]
    M. WEBER [1975], Minorations asymptotiques des trajectoires de fonctions aléatoires gaussiennes stationnaires définies sur l'intervalle [0,1]. C.R. Acad. Scienc. Paris Sér. A., pp. 49–52.Google Scholar

Copyright information

© Springer-Verlag 1977

Authors and Affiliations

  • Michel Weber

There are no affiliations available

Personalised recommendations