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

  • Makoto Maejima
Article

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.

Keywords

Characteristic Function Limit Theorem Central Limit Theorem Independent Random Variable Renewal Process 

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References

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    Cox, D. R. and Smith, W. L. (1953). A direct proof of a fundamental theorem of renewal theory,Skand. Aktuartidskr,36, 139–150.MathSciNetGoogle Scholar
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    Cramér, H. (1937).Random Variables and Probability Distributions, Cambridge University Press, Cambridge.Google Scholar

Copyright information

© The Institute of Statistical Mathematics 1975

Authors and Affiliations

  • Makoto Maejima
    • 1
  1. 1.Keio UniversityJapan

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