Skip to main content
SpringerLink
Log in

On local limit theorems and Blackwell's renewal theorem for independent random variables

  • Published:
Annals of the Institute of Statistical Mathematics Aims and scope Submit manuscript

Summary

Some types of local limit theorems for independent random variables are shown and the results obtained are applied to have generalizations of Blackwell's renewal theorem.

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

Similar content being viewed by others

References

  1. Williamson, J. A. (1965). Some renewal theorems for non-negative random variables,Trans. Amer. Math. Soc.,114, 417–445.

    Article  MathSciNet  Google Scholar 

  2. Maejima, M. (1972). A generalization of Blackwell's theorem for renewal processes to the case of non-identically distributed random variables,Rep. Statist. Appl. Res. JUSE,19, 1–9.

    MathSciNet  Google Scholar 

  3. Cox, D. R. and Smith, W. L. (1953). A direct proof of a fundamental theorem of renewal theory,Skand. Aktuartidskr,36, 139–150.

    MathSciNet  Google Scholar 

  4. Stone, C. (1965). A local limit theorem for nonlattice multi-dimensional distribution functions.Ann. Math. Statist,36, 546–551.

    MathSciNet  Google Scholar 

  5. Stone, C. (1967). On local and ratio limit theorems,Proc. Fifth Berkeley Symp. Math. Statist. Prob., II, Part 2, 217–224.

    Google Scholar 

  6. Cramér, H. (1937).Random Variables and Probability Distributions, Cambridge University Press, Cambridge.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Keio University, Japan

    Makoto Maejima

Authors
  1. Makoto Maejima
    View author publications

    You can also search for this author in PubMed Google Scholar

About this article

Cite this article

Maejima, M. On local limit theorems and Blackwell's renewal theorem for independent random variables. Ann Inst Stat Math 27, 507–520 (1975). https://doi.org/10.1007/BF02504668

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02504668

Keywords

Search

Navigation