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Tensor product of Gaussian measures

Part of the Lecture Notes in Mathematics book series (LNM,volume 644)

Keywords

  • Banach Space
  • Tensor Product
  • Gaussian Process
  • Sample Path
  • Gaussian Measure

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References

  1. T.W. ANDERSON-The integral of a symmetric unimodal function over a symmetric convex set and some probability inequalities. Proc. Amer. Math. Soc. 6 (1955) 170–176.

    CrossRef  MathSciNet  MATH  Google Scholar 

  2. A. BADRIKIAN — S. CHEVET — Mesures cylindriques, espaces de Wiener et fonctions aléatoires gaussiennes. Lecture Notes in Math. 379 (1974) Springer Verlag.

    Google Scholar 

  3. P. BAXENDALE-Gaussian measures on function spaces-Amer. J. of Math. 98 (1976) 891–952.

    CrossRef  MathSciNet  MATH  Google Scholar 

  4. R. CARMONA-Modul e de continuité uniforme des mouvements browniens à valeurs dans un espace de Banach. C.R. Acad. Sci. Paris ser. A 281 (1975) 659–662.

    MathSciNet  MATH  Google Scholar 

  5. R. CARMONA-N. KÔNO-Convergence en loi et lois du logarithme itéré pour les vecteurs gaussiens. Z. Wahrscheinlichkeits theorie verw. Gebiete 36 (1976) 241–267.

    CrossRef  MATH  Google Scholar 

  6. R. CARMONA-Measurable norms and some Banach space valued Gaussian processes. Duke Math. Journal 44 (1977) 109–127.

    CrossRef  MathSciNet  MATH  Google Scholar 

  7. S.D. CHATTERJI-A note on the convergence of Banach space valued martingales. Math. Ann. 153 (1964) 142–149.

    CrossRef  MathSciNet  MATH  Google Scholar 

  8. S. CHEVET-Un résultat sur les mesures gaussiennes. C.R. Acad. Sc. Paris Ser. A 284 (1977) 441–444.

    MathSciNet  MATH  Google Scholar 

  9. R.M. DUDLEY-The sizes of compact subsets of Hilbert space and continuity of Gaussian processes. J.Functional Analysis 1 (1967) 290–330.

    CrossRef  MathSciNet  MATH  Google Scholar 

  10. R.M. DUDLEY-J. FELDMAN-L. LE CAM-On semi-norms and probabilities and abstract Wiener spaces. Ann. of Math. 93 (1971) 390–408.

    CrossRef  MathSciNet  MATH  Google Scholar 

  11. X. FERNIQUE-Régularité des trajectoires des fonctions aléatoires gaussiennes. Lecture Notes in Math. 480 (1975) 1–96. Springer Verlag.

    CrossRef  MathSciNet  MATH  Google Scholar 

  12. L. GROSS-Measurable functions on Hilber space. Trans. Amer. Math. Soc. 105 (1962) 372–390.

    CrossRef  MathSciNet  MATH  Google Scholar 

  13. L. GROSS-Abstract Wiener Spaces. Proc. Fifth Berkeley Symp. on Math. Stat. and Prob. 2 (1965) 31–42.

    Google Scholar 

  14. L. GROSS-Potential theory on Hilbert Space. J. Functional Analysis 1 (1967) 123–181.

    CrossRef  MathSciNet  MATH  Google Scholar 

  15. G. KALLIANPUR-Abstract Wiener processes and their reproducing kernel Hilbert spaces. Z. Wahrscheinlichkeits theorie verw. Gebiete 17 (1971) 113–123.

    CrossRef  MathSciNet  MATH  Google Scholar 

  16. J. KUELBS-Gaussian measures on a Banach space. J. Functional Analysis 5 (1970) 354–367

    CrossRef  MathSciNet  MATH  Google Scholar 

  17. J. KUELBS-R.D. LE PAGE-The law of the iterated logarithm for Brownian motion in a Banach space. Trans. Amer. Math. Soc. 185 (1973) 253–264.

    CrossRef  MathSciNet  Google Scholar 

  18. H.H. KUO — Gaussian measures in Banach spaces. Lecture Notes in Math. 463 (1975) Springer Verlag.

    Google Scholar 

  19. H.H. KUO-Potential theory associated with Uhlenbeck-Ornstein process J. Functional Analysis. 21 (1976) 63–75.

    CrossRef  MathSciNet  MATH  Google Scholar 

  20. H.H. KUO-Distribution theory on Banach space-Lecture Notes in Math. 526 (1976) 143–156.

    CrossRef  MathSciNet  Google Scholar 

  21. M.B. MARCUS-L.A. SHEPP-Sample behavior of Gaussian processes. Proc. Sixth Berkeley Symp. on Math. Stat. and Prob. 2 (1970) 423–442.

    MathSciNet  Google Scholar 

  22. J. NEVEU — Processus aléatoires gaussiens — Les Presses de l'Université de Montréal 1968.

    Google Scholar 

  23. M.A. PIECH-Parabolic equations associated with the number operator. Trans. Amer. Math. Soc. 194 (1974) 213–222.

    CrossRef  MathSciNet  MATH  Google Scholar 

  24. M.A. PIECH-The Ornstein-Uhlenbeck Semi-Group in an infinite dimensional L2 — setting. J. Functional Analysis 18 (1975) 271–285.

    CrossRef  MathSciNet  MATH  Google Scholar 

  25. B.S. RAJPUT-On abstract Wiener measure-Nagoya Math. j. 46 (1972) 155–160.

    CrossRef  MathSciNet  MATH  Google Scholar 

  26. H. SATO-Gaussian measure on a Banach space and abstract Wiener space. Nagoya Math. J. 36 (1969) 65–83.

    CrossRef  MathSciNet  MATH  Google Scholar 

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© 1978 Springer-Verlag

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Carmona, R. (1978). Tensor product of Gaussian measures. In: Aron, R.M., Dineen, S. (eds) Vector Space Measures and Applications I. Lecture Notes in Mathematics, vol 644. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0066843

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  • DOI: https://doi.org/10.1007/BFb0066843

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  • Print ISBN: 978-3-540-08668-0

  • Online ISBN: 978-3-540-35906-7

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