Skip to main content
Log in

Gaussian approximation of mixing random fields

  • Published:
Acta Mathematica 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.

References

  1. I. Berkes and G. J. Morrow, Strong invariance principles for mixing random fields,Z. Wahrscheinlichkeitstheorie und verw. Gebiete,57 (1981), 15–37.

    Google Scholar 

  2. I. Berkes and W. Philipp, Approximation theorems for independent and weakly dependent random vectors,Annals of Probability,7 (1979), 29–54.

    Google Scholar 

  3. Yu. A. Davidov, The invariance principle for stationary processes,Theor. Probability Appl.,15 (1970), 487–498.

    Google Scholar 

  4. R. L. Dobrushin and P. Major, Non-central limit theorems for non-linear functionals of Gaussian fields,Z. Wahrscheinlichkeitstheorie und verw. Gebiete,50 (1979), 27–52.

    Google Scholar 

  5. A. Dvoretzky, Asymptotic normality for sums of dependent random variables,Proc. Sixth Berkeley Sympos. Math. Statist. Probab. Vol. II, 513–535, Univ. of California Press (1970).

  6. I. A. Ibraginov, Some limit theorems for stationary processes,Theor. Probability Appl.,7 (1962), 349–382.

    Google Scholar 

  7. A. N. Kolmogorov and Yu. A. Rozanov, On strong mixing conditions for stationary Gaussian random processes,Theor. Probability Appl.,5 (1960), 204–208.

    Google Scholar 

  8. J. Kuelbs and W. Philipp, Almost sure invariance principles for partial sums of mixing B-valued random variables,Annals of Probability,8 (1980), 1003–1036.

    Google Scholar 

  9. M. Loève,Probability Theory, Van Nostrand (Toronto-New York-London, 1955).

    Google Scholar 

  10. F. Móricz, Moment inequalities for the maximum of partial sums of random fields,Acta Math. Acad. Sci. Hungar.,39 (1977), 353–366.

    Google Scholar 

  11. F. Móricz, Exponential estimates for the maximum of partial sums II (Random fields),Acta math. Acad. Sci. Hungar.,35 (1980), 361–377.

    Google Scholar 

  12. G. J. Morrow, Invariance principles for Gaussian sequences,Z. Wahrscheinlichkeitstheorie und verw. Gebiete,52 (1980), 115–126.

    Google Scholar 

  13. W. Philipp and W. F. Stout, Almost sure invariance principles for partial sums of weakly dependent random variables,Memoirs of the Amer. Math. Soc. No. 161 (Providence, R. I., 1975).

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Berkes, I. Gaussian approximation of mixing random fields. Acta Math Hung 43, 153–185 (1984). https://doi.org/10.1007/BF01951335

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01951335

Keywords

Navigation