Skip to main content
Log in

An A.S. Invariance principle for lacunary seriesf(n k x)

  • Published:
Acta Mathematica Academiae Scientiarum Hungarica Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. I. Berkes, On the asymptotic behaviour of Σf(n k x) I. Main theorems,Zeitschrift für Wahrscheinlichkeitstheorie verw. Gebiete,34 (1976), 319–345.

    Google Scholar 

  2. I. Berkes, On the asymptotic behaviour of Σf(n k x) II. Applications,Zeitschrift für Wahrscheinlichkeitsthoorie verw. Gebiete,34 (1976), 347–365.

    Google Scholar 

  3. V. F. Gaposhkin, On the central limit theorem for some weakly dependent sequences (in Russian),Teor. Verojatn. i Primenen,15 (1970), 666–684. English translation:Theory Prob. and Appl.,15 (1970), 649–666.

    Google Scholar 

  4. M. Kac, On the distribution of values of sums of the type Σf(2k t),Ann. Math.,47 (1946), 33–49.

    Google Scholar 

  5. M. Kac, Probability methods in some problems of analysis and number theory,Bull. Amer. Math. Soc.,55 (1949), 641–665.

    Google Scholar 

  6. W. Philipp andW. F. Stout, Almost sure invariance principles for partial sums of weakly dependent random variables.Memoirs of the AMS, no. 161.

  7. V. Strassen, Almost sure behaviour of sums of independent random variables and martingales,Proc. 5th Berkeley Sympos. Math. Statist. and Probab. Vol. II. (Part I), 315–343, Univ. of California Press (Berkeley, 1967).

    Google Scholar 

  8. S. Takahashi, The law of the iterated logarithm for a gap sequence with infinite gaps,Tohoku Math. Journ.,15 (1963), 281–288.

    Google Scholar 

  9. A. Zygmund,Trigonometric series, Vol. I., Cambridge University Press (1959).

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Berkes, I., Philipp, W. An A.S. Invariance principle for lacunary seriesf(n k x) . Acta Mathematica Academiae Scientiarum Hungaricae 34, 141–155 (1979). https://doi.org/10.1007/BF01902603

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01902603

Keywords

Navigation