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Probability Theory and Related Fields

, Volume 77, Issue 4, pp 471–479 | Cite as

A strong renewal theorem for generalized renewal functions in the infinite mean case

  • Kevin K. Anderson
  • Krishna B. Athreya
Article

Summary

LetF(x) be a nonarithmetic c.d.f. on (0, ∞) such that 1 —F(x)=x−αL(x), whereL(x) is slowly varying and 0≤α≤1. Leta(x) be regularly varying with exponent β≥1. A strong renewal theorem (of Blackwell type) for generalized renewal functions of the form\(G(t) \equiv \sum\limits_{n = 0}^\infty {a(n) F^n (t)} \) is proved here, thus extending the recent work of Embrechts, Maejima and Omey [1] and that of Erickson [4].

Keywords

Recent Work Stochastic Process Probability Theory Mathematical Biology Generalize Renewal 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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Copyright information

© Springer-Verlag 1988

Authors and Affiliations

  • Kevin K. Anderson
    • 1
  • Krishna B. Athreya
    • 1
  1. 1.Department of Mathematics and StatisticsIowa State UniversityAmesUSA

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