Skip to main content
Log in

Large deviations for sums of random variables connected into a Markov chain in approximation by Poisson law

  • Published:
Lithuanian Mathematical Journal 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. Aleškevičienè and V. Statulevičius, Large deviations in approximation by Poisson approximation, in:Probability Theory and Mathematical Statistics, Proceedings of the Sixth Vilnius Conference, Grigelioniset al. (Eds.), VSP/TEV (1994), pp. 1–18.

  2. A. Aleškevičienè and V. Statulevičius, Large deviations in power zones in approximation by Poisson law,Uspekhi Mat. Nauk,50, 63–82 (1995).

    Google Scholar 

  3. P. Deheuvels, Large deviations by Poisson approximation,J. Statist. Plann. Inference,32, 75–88 (1992).

    Article  MATH  MathSciNet  Google Scholar 

  4. H. Y. Chen Louis, Poisson approximation for dependent trials,Ann. Probab.,3, 534–545 (1975).

    Google Scholar 

  5. H. Y. Chen Louis and R. P. Choi, Some asymptotic and large deviations results in Poisson approximation,Ann. Probab.,20, 1867–1876 (1992).

    MathSciNet  Google Scholar 

  6. V. Sidoravičius and V. Statulevičius, Convergence to the Poisson law on algebraic structures for ψ-mixing systems, in:Proceedings of the 6th USSR-Japan Symposium, World Sci. Publ., Kiev-Singapore (1995), pp. 354–365.

    Google Scholar 

  7. P. Gudynas, OnO B-regularity of a homogeneous Markov chain,Liet. Matem. Rink.,22, 67–80 (1982).

    MATH  MathSciNet  Google Scholar 

  8. P. Gudynas, On convergence to the Poisson law for distributions of sums of random variables connected into a chain,Lith. Math. J.,35, 234–242 (1995).

    MATH  MathSciNet  Google Scholar 

  9. T. Kato,Perturbation Theory for Linear Operators, Springer-Verlag, Berlin-Heidelberg-New York (1966).

    Google Scholar 

Download references

Authors

Additional information

Institute of Mathematics and Informatics, Akademijos 4, 2600 Vilnius, Lithuania. Translated from Lietuvos Matematikos, Rinkinys, Vol. 37, No. 1, pp. 26–37, January–March, 1997.

Translated by V. Mackevičius

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gudynas, P. Large deviations for sums of random variables connected into a Markov chain in approximation by Poisson law. Lith Math J 37, 20–28 (1997). https://doi.org/10.1007/BF02465436

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02465436

Keywords

Navigation