Skip to main content

Norms of Gaussian sample functions

Part of the Lecture Notes in Mathematics book series (LNM,volume 550)

Keywords

  • Linear Space
  • Gaussian Process
  • Lipschitz Condition
  • Gaussian Measure
  • Admissible Pair

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   44.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   59.00
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. R.M. Dudley, Sample functions of the Gaussian proces, Ann. Probability, 1, 1, 1973, pp. 66–103.

    CrossRef  MathSciNet  MATH  Google Scholar 

  2. X. Fernique, Régularité de processus gaussiens, Invent. Math., 12, 4, 1971, pp. 304–320.

    CrossRef  MathSciNet  MATH  Google Scholar 

  3. J. Hoffmann-Jørgensen, Sums of independent Banach space valued random variables, Studia Math., 52, 2, 1974, pp. 159–186.

    MathSciNet  MATH  Google Scholar 

  4. K. Itô, M. Nisio, On the oscillation functions of Gaussian processes, Math. Scand., 22, 1, 1968, pp. 209–223.

    MathSciNet  MATH  Google Scholar 

  5. M.B. Marcus and L.A. Shepp, Sample behavior of Gaussian processes, Proc. Sixth Berkeley Symp. Math. Statist. Probability, Vol. 2, 1972, pp. 423–441, Univ. Calif. Press.

    MathSciNet  MATH  Google Scholar 

  6. B.J. Pettis, On integration in vector spaces, Trans. Amer. Math. Soc., 44, 2, 1938, pp. 277–304.

    CrossRef  MathSciNet  MATH  Google Scholar 

  7. A.M. Veršik, The axiomatics of measure theory in linear spaces, Dokl. Akad. Nauk SSSR, 178, 2, 1968, pp. 278–281. English translation in: Soviet Math.Dokl., 9, 1, 1968, pp. 68–72.

    MathSciNet  Google Scholar 

  8. S.M. Nikol'skii, Approximation of several variables and embedding theorems, Moscow, 1969(Russian)

    Google Scholar 

  9. V.A. Rohlin, On the fundamental ideas of measure theory, Mat. Sb., 25(67), 1, 1949, pp. 107–150. English translation in: Amer. Math. Soc. Translation, 71 (1952).

    MathSciNet  Google Scholar 

  10. V.N. Sudakov, B.S. Girel'son. Extremal properties of half-spaces for spherically symmetrical measures, Zap. Naucn. Sem. Leningrad. Otdel. Mat. Inst. Steklov (LOMI), 41, 1974, pp. 14–24. (Russian)

    MathSciNet  Google Scholar 

  11. B.S. Cirel'son, Some properties of lacunary series and Gaussian measures connected with uniform variants of the Egoroff and Lusin properties, Teor. Verojatnost. i Primenen., 20, 3, 1975, pp. 664–667 (Russian).

    MathSciNet  Google Scholar 

  12. B.S. Cirel'son, The density of the distribution of the maximum of a Gaussian process, Teor. Verojatnost. i Primenen., 20, 4, 1975, pp. 567–575 (Russian).

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1976 Springer-Verlag

About this paper

Cite this paper

Cirel'son, B.S., Ibragimov, I.A., Sudakov, V.N. (1976). Norms of Gaussian sample functions. In: Maruyama, G., Prokhorov, J.V. (eds) Proceedings of the Third Japan — USSR Symposium on Probability Theory. Lecture Notes in Mathematics, vol 550. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0077482

Download citation

  • DOI: https://doi.org/10.1007/BFb0077482

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-07995-8

  • Online ISBN: 978-3-540-37966-9

  • eBook Packages: Springer Book Archive