Random Fourier series on locally compact abelian groups

Michael B. Marcus; Gilles Pisier

Séminaire de probabilités de Strasbourg (1979)

  • Volume: 13, page 72-89

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Marcus, Michael B., and Pisier, Gilles. "Random Fourier series on locally compact abelian groups." Séminaire de probabilités de Strasbourg 13 (1979): 72-89. <http://eudml.org/doc/113262>.

@article{Marcus1979,
author = {Marcus, Michael B., Pisier, Gilles},
journal = {Séminaire de probabilités de Strasbourg},
keywords = {random Fourier series; locally compact Abelian group; stationary Gaussian processes; processes with sub-Gaussian increments},
language = {eng},
pages = {72-89},
publisher = {Springer - Lecture Notes in Mathematics},
title = {Random Fourier series on locally compact abelian groups},
url = {http://eudml.org/doc/113262},
volume = {13},
year = {1979},
}

TY - JOUR
AU - Marcus, Michael B.
AU - Pisier, Gilles
TI - Random Fourier series on locally compact abelian groups
JO - Séminaire de probabilités de Strasbourg
PY - 1979
PB - Springer - Lecture Notes in Mathematics
VL - 13
SP - 72
EP - 89
LA - eng
KW - random Fourier series; locally compact Abelian group; stationary Gaussian processes; processes with sub-Gaussian increments
UR - http://eudml.org/doc/113262
ER -

References

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  1. [1] Belyaev, Yu.K., Continuity and Hölder's conditions for sample functions of stationary Gaussian processes, Proc. Fourth Berkeley Symp. Math. Statist. Prob.2 (1961), 22-33. Zbl0111.33003
  2. [2] Dudley, R.M.The sizes of compact subsets of Hilbert space and continuity of Gaussian processes, J. Funct. Anal.1 (1967), 290-330. Zbl0188.20502MR220340
  3. [3] Fernique, X., Régularité des trajectories des fonctions aléatoires gaussiennes, Lecture Notes in Mathematics, 480, 1975, 1-96. Zbl0331.60025MR413238
  4. [4] Jain, N.C.and Marcus, M.B., Sufficient conditions for the continuity of stationary Gaussian processes and applications to random series of functions, Ann. Inst. Fourier (Grenoble) 24 (1974), 117-141. Zbl0283.60041MR413239
  5. [5] Jain, N.C.and Marcus, M.B., Continuity of subgaussian processes, Advances in Probability, Vol. 5, M. Dekker. MR515431
  6. [6] Kahane, J.P., Some random series of functions, 1968, D. C. Heath, Lexington, Mass. Zbl0192.53801MR254888
  7. [7] Marcus, M.B., Continuity and the central limit theorem for random trigonometric series, Z. Warscheinlichkeitsth., 42 (1978), 35-56. Zbl0382.60041MR486035
  8. [8] Marcus, M.B.and Pisier, G., Necessary and sufficient conditions for the uniform convergence of random trigonometric series, Lecture Note Series, 1978, Arhus University, Denmark. Zbl0409.60036MR507061
  9. [9] Paley, R.E.A.C.and Zygmund, A., On series of functions (1) (2) (3), Proceedings of Cambridge Phil. Soc.26 (1930), 458-474, 28 (1932), 190-205. Zbl0006.19802JFM56.0254.01
  10. [10] Pisier, G., Sur l'espace de Banach des series de Fourier aleatoire presque surement continué, Exposé No. 17-18, Séminaire Maurey-Schwartz1977-78, Ecole Polytechnique Paris. MR520216
  11. [11] Salem, R. and Zygmund, A.Some properties of trigonometric series whose terms have random signs, Acta Math.91 (1954), 245-301. Zbl0056.29001MR65679
  12. [12] Jain, N.C.and Marcus, M.B., Integrability of infinite sums of independent vector-valued random variables, Trans. Amer. Math. Soc.212 (1975), 1-36. Zbl0318.60036MR385995
  13. [13] Fernique, X., Des rèsultats nouveaux sur les processus gaussiens, C. R. Acad. Sci.Paris Ser. A278 (1974), 363-365. Zbl0274.60029MR413237

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