Skip to main content

Almost sure invariance principles for empirical distribution functions of weakly dependent random variables

  • 346 Accesses

Part of the Lecture Notes in Mathematics book series (LNM,volume 566)

Keywords

  • Unit Ball
  • Limit Point
  • Invariance Principle
  • Reproduce Kernel Hilbert Space
  • Iterate Logarithm

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   29.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   39.99
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

  • Aronszajn, N. (1950), The theory of reproducing kernels, Trans. Amer. Math. Soc. 68, 337–404.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • Berkes, István (1975), On the asymptotic behavior of ∑ f(nk, x) parts I + II, Z. Wahrscheinl, verw. Geb. 34, 319–365.

    CrossRef  MathSciNet  Google Scholar 

  • Billingsley, Patrick (1967), unpublished manuscript.

    Google Scholar 

  • Billingsley, Patrick (1968), Convergence of probability measures, Wiley, New York.

    MATH  Google Scholar 

  • Cassels, J. W. S. (1951), An extension of the law of the iterated logarithm, Proc. Cambridge Philos. Soc. 47, 55–64.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • Chover, J. (1967), On Strassen's version of the log log law, Z. Wahrscheinl. verw. Geb. 8, 83–90.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • Chung, K.-L. (1949), An estimate concerning the Kolmogoroff limit distribution, Trans. Amer. Math. Soc. 67, 36–50.

    MathSciNet  MATH  Google Scholar 

  • Donsker, M. (1952), Justification and extension of Doob's heuristic approach to the Kolmogorov-Smirnov theorems, Ann. Math. Stat. 23, 277–281.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • Erdős, P. (1964), Problems and results on diophantine approximations, Compositio Math 16, 52–65.

    MathSciNet  MATH  Google Scholar 

  • Erdös, P. and Gál, I. S., On the law of the iterated logarithm, Proc. Koninkl. Nederl. Akad Wetensch. Ser. A 58, 65–84.

    Google Scholar 

  • Finkelstein, Helen (1971), The law of the iterated logarithm for empirical distributions, Ann. Math. Stat. 42, 607–615.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • Meschkowski, Herbert (1962), Hilbertsche Räume mit Kernfunktionen, Springer, Berlin.

    CrossRef  MATH  Google Scholar 

  • Oodaira, Hiroshi (1975), Some functional laws of the iterated logarithm for dependent random variables, Colloqu. Math. Soc. János Bolyai 11, 253–272.

    MathSciNet  MATH  Google Scholar 

  • Philipp, Walter (1975), Limit theorems for lacunary series and uniform distribution mod 1, Acta Arithmetica 26, 241–251.

    MathSciNet  MATH  Google Scholar 

  • Philipp, Walter and Stout, William (1975), Almost sure invariance principles for partial sums of weakly dependent random variables, Memoirs Amer. Math. Soc. 161.

    Google Scholar 

  • Riesz, F. and Sz. Nagy, B. (1955), Functional analysis, Frederick Unger, New York.

    MATH  Google Scholar 

  • Smirnoff, N. (1939), Sur les ecarts de le courbe de distribution coupirique. Mat. Sbornik 6, 3–26.

    MathSciNet  MATH  Google Scholar 

  • Stout, W. F. (1974), Almost sure convergence. Academic Press, New York.

    MATH  Google Scholar 

  • Strassen, V. (1965), An invariance principle for the law of the iterated logarithm. Z. Wahrscheinl. 3, 211–226.

    CrossRef  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

Philipp, W. (1976). Almost sure invariance principles for empirical distribution functions of weakly dependent random variables. In: Gaenssler, P., Révész, P. (eds) Empirical Distributions and Processes. Lecture Notes in Mathematics, vol 566. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0096881

Download citation

  • DOI: https://doi.org/10.1007/BFb0096881

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-08061-9

  • Online ISBN: 978-3-540-37515-9

  • eBook Packages: Springer Book Archive