Continuity and the central limit theorem for random trigonometric series

  • Michael B. Marcus


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Calderon, A.P.: Intermediate spaces and interpolation the complex method. Studia Math. 24, 113–190 (1964)Google Scholar
  2. 2.
    Dudley, R.M.: The sizes of compact subsets of Hilbert space and continuity of Gaussian processes. J. Functional Analysis 1, 290–330 (1967)Google Scholar
  3. 3.
    Fernique, X.: Des résultats nouveaux sur les processus gaussiens. C.R. Acad. Sci. Paris Sér. A 278, 363–365 (1974)Google Scholar
  4. 3a.
    Fernique, X.: Regularité des trajectoires des functions aléatoires gaussiennes. Lecture Notes in Math., 480. Berlin: Springer 1975Google Scholar
  5. 4.
    Garsia, A.M., Rodemich, E.: Monotonicity of certain functionals under rearrangements. Ann. Inst. Fourier (Grenoble) 24, 67–116 (1974)Google Scholar
  6. 5.
    Hoffman-Jørgensen, J.: Sums of independent Banach space valued random variables. Studia Math. 52, 159–186 (1974)Google Scholar
  7. 6.
    Jain, N.C., Marcus, M.B.: Sufficient conditions for the continuity of stationary Gaussian processes and applications to random series of functions. Ann. Inst. Fourier 24, 117–141 (1974)Google Scholar
  8. 7.
    Jain, N.C., Marcus, M.B.: Integrability of infinite sums of independent vector-valued random variables. Trans. Amer. Math. Soc. 212, 1–36 (1975)Google Scholar
  9. 8.
    Jain, N.C., Marcus, M.B.: Central limit theorems for C(S)-valued random variables. J. Functional Analysis 19, 216–231 (1975)Google Scholar
  10. 9.
    Kahane, J.P.: Some random series of functions. Lexington, Mass.: D.C. Heath 1968Google Scholar
  11. 10.
    Marcus, M.B.: Uniform convergence of random Fourier series, Ark. Mat. 13, 107–122 (1975)Google Scholar
  12. 11.
    Salem, R., Zygmund, A.: Some properties of trigonometric series whose terms have random signs. Acta Math. 91, 245–301 (1954)Google Scholar
  13. 12.
    Marcus, M.B.: Lecture notes on Gaussian processes. Center for Probability and Statistics, Northwestern University (1977).Google Scholar

Copyright information

© Springer-Verlag 1978

Authors and Affiliations

  • Michael B. Marcus
    • 1
  1. 1.Northwestern UniversityEvanstonUSA

Personalised recommendations