SpringerLink
Log in

Limit theorems and phase transitions for two models of summation of iid random variables depending on parameters

  • Mathematics
  • Published:
Doklady Mathematics 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

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Instant access to the full article PDF.

Institutional subscriptions

References

  1. G. Ben Arous, L. V. Bogachev, and S. A. Molcahnov, Probab. Theory Rel. Fields 132, 579–612 (2005).

    Article  MATH  Google Scholar 

  2. L. V. Bogachev, CRM Proc. Lect. Notes 42, 41–64 (2007).

    MathSciNet  Google Scholar 

  3. A. Bovier, I. Kurkova, and M. Löwe, Ann. Probab. 30, 605–651 (2002).

    Article  MathSciNet  MATH  Google Scholar 

  4. D. Brockmann and L. Hufnagel, in Complex Population Dynamics: Nonlinear Modeling in Ecology, Epidemiology, and Genetics (World Scientific, Singapore, 2007), pp. 109–127.

    Book  Google Scholar 

  5. J. M. Bullock and R. T. Clarke, Oecologia 124, 506–521 (2000).

    Article  Google Scholar 

  6. A. Chakrabarty and M. M. Meerschaert, Stat. Probab. Lett. 81, 989–997 (2011).

    Article  MathSciNet  MATH  Google Scholar 

  7. A. Chakrabarty and G. Samorodnitsky, Stoch. Models 28(1), 109–143 (2012).

    Article  MathSciNet  MATH  Google Scholar 

  8. M. Cranston and S. A. Molchanov, Israel J. Math. 148, 115–136 (2005).

    Article  MathSciNet  MATH  Google Scholar 

  9. B. Derrida, Phys. Rev. Lett. 45, 79–82 (1980).

    Article  MathSciNet  Google Scholar 

  10. M. Grabchak, J. Theor. Probab. (2013) [in press].

    Google Scholar 

  11. M. Grabchak, Limit Theorems for Sequences of Tempered Stable and Related Distributions (2012). http://arxiv.org/abs/1201/6006.

    Google Scholar 

  12. M. Grabchak, J. Appl. Probab. 49, 1015–1035 (2012).

    Article  MathSciNet  MATH  Google Scholar 

  13. M. Grabchak and G. Samorodnitsky, Quant. Finance 10, 883–893 (2010).

    Article  MathSciNet  MATH  Google Scholar 

  14. B. Jorgensen, J. R. Martinez, and V. Vinogradov, Lith. Math. J. 49, 399–425 (2009).

    Article  MathSciNet  Google Scholar 

  15. J. Rosiński, Stoch. Proc. Appl. 117, 677–707 (2007).

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. The University of North Carolina, Charlotte, USA

    M. Grabchak & S. A. Molchanov

Authors
  1. M. Grabchak
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. S. A. Molchanov
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Published in Russian in Doklady Akademii Nauk, 2013, Vol. 451, No. 4, pp. 374–377.

The article was translated by the authors.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Grabchak, M., Molchanov, S.A. Limit theorems and phase transitions for two models of summation of iid random variables depending on parameters. Dokl. Math. 88, 431–434 (2013). https://doi.org/10.1134/S1064562413030204

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1064562413030204

Keywords

Search

Navigation