Skip to main content
SpringerLink
Log in

Asymptotics of infinitely divisible distributions onR

  • Published:
Siberian 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

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Literature Cited

  1. E. Lukach Characteristic Functions, Griffin, London (1970).

    Google Scholar 

  2. V. P. Chistyakov, “A theorem on sums of positive random variables and its application to branching random processes,” Teor. Veroyatn. Primen.,9, No. 4, 710–718 (1964).

    Google Scholar 

  3. J. Chover, P. Ney, and S. Wainger, “Degeneracy properties of subcritical branching processes,” Ann. Probab.,1, No. 4, 663–673 (1973).

    Google Scholar 

  4. P. Embrechts, C. M. Goldie, and N. Veraverbeke, “Subexponentiality and infinite divisibility,” Z. Wahrscheinlichkeitstheor. Geb.,49, No. 3, 335–347 (1979).

    Google Scholar 

  5. P. Embrechts and C. M. Goldie, “On convolution tails,” Stoch. Proc. Appl.,13, No. 3, 263–278 (1982).

    Google Scholar 

  6. I. F. Pinelis, “On asymptotic equivalence of probabilities of large deviations of a sum and the maximum of independent random variables,” in: Predel'n. Teor. Teor. Veroyatn. Trans. Math. Inst. Sib. Branch, Academy of Sciences of the USSR, Nauka Novosibirsk,5, 144–173 (1985).

    Google Scholar 

  7. M. S. Sgibnev, “Banach algebras of measures of the classg(γ),” Sib. Mat. Zh.,29, No. 4, 162–171 (1988).

    Google Scholar 

  8. V. M. Kruglov, “A remark on the theory of infinitely divisible laws,” Teor. Veroyatn. Primen.,15, No. 2, 330–336 (1970).

    Google Scholar 

  9. G. E. Shilov, “On locally analytic functions,” Usp. Mat. Nauk,21, No. 6, 177–182 (1966).

    Google Scholar 

  10. J. R. Blum and M. Rosenblatt, “On the structure of infinitely divisible distributions,” Pacific J. Math.,9, No. 1, 1–7 (1959).

    Google Scholar 

  11. W. Rudin, Functional Analysis, McGraw-Hill (1972).

  12. V. M. Zolotarev, “On the asymptotic behavior of a class of infinitely divisible distribution laws,” Teor. Veroyatn. Primen.,6, No. 3, 330–334 (1961).

    Google Scholar 

  13. A. M. Ulanovskii, “On the asymptotic behavior of infinitely divisible distributions at infinity,” Teor. Funkts. Funkts. Anal. Prilozh., Kharkov,35, 100–107 (1981).

    Google Scholar 

  14. V. M. Kruglov and S. N. Antonov, “On the asymptotic behavior of infinitely divisible distributions in a Banach space,” Teor. Veroyatn. Primen.,27, No. 4, 624–642 (1982).

    Google Scholar 

  15. V. M. Krugov and S. N. Antonov, “Once again on the asymptotic behavior of infinitely divisible distributions in a Banach space,” Teor. Veroyatn. Primen.,29, No. 4, 732–742 (1984).

    Google Scholar 

  16. V. M. Kruglov, Additional Chapters in Probability Theory [in Russian], Vysshaya Shkola, Moscow (1984).

    Google Scholar 

  17. A. L. Yakimov, “Asymptotic behavior of a class of infinitely divisible distributions,” Teor. Veroyatn. Primen.,32, No. 4, 691–702 (1987).

    Google Scholar 

  18. R. Grübel, “On subordinated distributions and generalized renewal measures,” Ann. Probab.,15, No. 1, 394–415 (1987).

    Google Scholar 

  19. R. Grübel, “Uber unbegrenzt teilbare Verteilungen,” Arch. Math.,41, No. 1, 80–88 (1983).

    Google Scholar 

  20. R. Grübel, “Functions of discrete probability measures: Rates of convergence in the renewal theorem,” Z. Wahrscheinlichkeitstheor. Geb.,64, 341–357 (1983).

    Google Scholar 

Download references

Authors
  1. M. S. Sgibnev
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Novosibirsk. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 31, No. 1, pp. 135–140, January–February, 1990.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Sgibnev, M.S. Asymptotics of infinitely divisible distributions onR . Sib Math J 31, 115–119 (1990). https://doi.org/10.1007/BF00971156

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00971156

Keywords

Search

Navigation