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Regularity of gaussian processes

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References

  1. Badrikian, A. &Chevet, S.,Mesures cylindriques, espaces de Wiener et fonctions aléatoires Gaussiennes. Lecture Notes in Math., 379 (1974), Springer-Verlag, New York.

    MATH  Google Scholar 

  2. Borell, C., The Brunn-Minkowski inequality in Gauss space.Invent. Math., 30 (1975), 205–216.

    Article  MathSciNet  Google Scholar 

  3. Dudley, R. M., The size of compact subsets of Hilbert space and continuity of Gaussian processes.J. Funct. Anal., (1967), 290–330.

  4. —, Sample functions of the Gaussian process.Ann. Probab., 1 (1973), 66–103.

    MATH  MathSciNet  Google Scholar 

  5. Feldman, J., Sets of boundedness and continuity for the canonical normal process.Proc. Sixth Berkeley Symposium 1971, p. 357–367. University of California Press.

  6. Fernique, X., Continuité des processus Gaussiens.C. R. Acad. Sci. Paris, 258 (1964), 6058–6060.

    MATH  MathSciNet  Google Scholar 

  7. —, Intégrabilité des vecteurs Gaussiens.C. R. Acad. Sci. Paris, 270 (1970), 1698–1699.

    MATH  MathSciNet  Google Scholar 

  8. —, Certaines propriétés des éléments aléatoires Gaussiens.Symposia Mathematica, Vol. IX, p. 37–42. Academic Press, London 1972.

    Google Scholar 

  9. —, Minoration des fonctions aléatoires Gaussiennes.Colloque International sur les processus Gaussiens et les distributions aleatoires.Ann. Inst. Fourier, 24 (1974), 61–66.

    MATH  MathSciNet  Google Scholar 

  10. Fernique, X., Regularité des trajectoires des fonctions aléatoires Gaussiennes.Lecture Notes in Math., 480 (1974), 1–96. Springer Verlag.

  11. Fernique, X., Evaluation de processus Gaussiens composés.Lecture Notes in Math., 526 (1976), 67–83. Springer Verlag.

  12. —, Evaluation de certaines fonctionnelles associées à des fonctions aléatoires Gausiennes.Probab. Math. Statist. 2 (1981), 1–29.

    MATH  MathSciNet  Google Scholar 

  13. —, Sur la convergence étroite des mesures Gaussiennes.Z. Wahrsch. Verw. Gebiete, 68 (1985), 331–336.

    Article  MATH  MathSciNet  Google Scholar 

  14. Garsia, A. M., Continuity properties of Gaussian processes with multidimensional time parameter.Proc. Sixth Berkley Symphosium 1971, p. 369–374. University of California Press.

  15. Garsia, A. M., Rodemich, E. &Rumsey, Jr., H., A real variable lemma and the continuity of paths of some Gaussian processes.Indiana Univ. Math. J., 20 (1970), 565–578.

    Article  MathSciNet  MATH  Google Scholar 

  16. Heinkel, B., Théorème central-limite et loi du logarithme itéré dansC(S).C.R. Acad. Sci. Paris, 282 (1976), 711–713.

    MATH  MathSciNet  Google Scholar 

  17. Heinkel, B., Mesures majorantes et régularité de fonctions aléatoires.Colloques Internationaux du CNRS No. 307 (“Aspects statistiques et aspects physiques des processus Gaussiens”). 1980, p. 407–434.

  18. Jain, N. C. &Marcus, M. B., Central limit theorem forC(S) valued random variables.J. Funct. Anal., 19 (1975), 216–231.

    Article  MathSciNet  MATH  Google Scholar 

  19. Landau, H. &Shepp, L. A., On the supremum of a Gaussian process.Sankhyã, 32 (1970), 369–378.

    MathSciNet  MATH  Google Scholar 

  20. Marcus, M. B. & Shepp, L. A., Sample behavior of Gaussian processes.Proc. Sixth Berkeley Symphosium 1971, p. 423–441. University of California Press.

  21. Marcus, M. B. & Pisier, G.,Random Fourier series with application to harmonic analysis. Ann. Math. Studies 101, 1981. Princeton Univ. Press.

  22. —, Characterizations of almost surely continuousp-stable random Fourier series and strongly stationary processes.Acta. Math., 152 (1984), 245–301.

    MATH  MathSciNet  Google Scholar 

  23. Preston, C., Banach spaces arising from some integral inequalities.Indiana Univ. Math. J., 20 (1971), 997–1015.

    Article  MATH  MathSciNet  Google Scholar 

  24. Slepian, D., The one sided barrier problem for Gaussian noise.Bell Systems Tech. J., 41 (1962), 463–501.

    MathSciNet  Google Scholar 

  25. Sudakov, V. N., Gaussian measures, Cauchy measures and ε-entropy.Soviet Math. Dokl., 10 (1969), 310.

    MATH  Google Scholar 

  26. —, Gaussian random processes and measures of solid angles in Hilbert spaces.Soviet Math. Dokl., 12 (1971), 412–415.

    MATH  MathSciNet  Google Scholar 

  27. —, A remark on the criterion of continuity of Gaussian sample functions.Lecture Notes in Math., 330 (1973), 444–454.

    Article  MATH  MathSciNet  Google Scholar 

  28. Talagrand, M., Regularité des processus Gaussiens.C.R. Acad. Sci. Paris, 301 (1985), 379–381.

    MATH  MathSciNet  Google Scholar 

  29. —, La description des processus Gaussiens bornés.C.R. Acad. Sci. Paris, 301 (1985), 751–753.

    MATH  MathSciNet  Google Scholar 

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Talagrand, M. Regularity of gaussian processes. Acta Math. 159, 99–149 (1987). https://doi.org/10.1007/BF02392556

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  • DOI: https://doi.org/10.1007/BF02392556

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