Skip to main content
Log in

A strong approximation theorem for sums of random vectors in the domain of attraction to a stable law

  • 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. A. de Acosta and E. Giné, Convergence of moments and related functionals in the general central limit theorem in Banach spaces,Z. Wahrscheinlichkeitstheorie verw. Gebiete,48 (1979), 213–231.

    Article  Google Scholar 

  2. J. Banys, On the convergence rate in the multidimensional local limit theorem with limiting stable law,Litovskii Mat. Sbornik,16 (1976), 13–20 (in Russian); English translation:Lithuanian Math. J.,16 (1976), 320–325.

    Google Scholar 

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

    Google Scholar 

  4. P. Billingsley,Convergence of probability measures, J. Wiley (New York, 1968).

    Google Scholar 

  5. A. Dabrowski, H. Dehling and W. Philipp, An almost sure invariance principle for triangular arrays of Banach space valued random variables.Z. Wahrscheinlichkeitstheorie verw. Gebiete,65 (1984), 483–491.

    Article  Google Scholar 

  6. W. Feller, A limit theorem for random variables with infinite moments,Amer. J. Math.,68 (1946), 257–262.

    Google Scholar 

  7. C. C. Heyde, A note concerning behavior of iterated logarithm type,Proc. Amer. Math. Soc.,23 (1969), 85–90.

    Google Scholar 

  8. P. Lévy,Théorie de l'addition des variables aléatoires. Gauthiers-Villars (Paris, 1937).

    Google Scholar 

  9. M. Loéve,Probability Theory, 2nd ed., Van Nostrand(Princeton, N. J., 1963).

    Google Scholar 

  10. W. Philipp, Weak andL P-invariance principles for sums of B-valued random variables,Ann. Probability,8 (1980), 68–82; Correction,ibid.Ann. Probability 14 (1986).

    Google Scholar 

  11. W. Philipp, Almost sure invariance principles for sums ofB-valued random variables,Probability in Banach spaces II (Proc. Conf. Oberwolfach, 1978), Lecture Notes in Math. 709, Springer (Berlin-Heidelberg-New York, 1979), pp. 171–193.

    Google Scholar 

  12. W. F. Stout, Almost sure invariance principles whenEX 1=∞2 Z. Wahrscheinlichkeitstheorie verw. Gebiete,44 (1979), 23–32.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Berkes, I., Dabrowski, A., Dehling, H. et al. A strong approximation theorem for sums of random vectors in the domain of attraction to a stable law. Acta Math Hung 48, 161–172 (1986). https://doi.org/10.1007/BF01949061

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01949061

Keywords

Navigation