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


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].


Recent Work Stochastic Process Probability Theory Mathematical Biology Generalize Renewal 
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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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