Almost Sure Convergence of Renewal Processes

  • Valeriĭ V. Buldygin
  • Karl-Heinz Indlekofer
  • Oleg I. Klesov
  • Josef G. Steinebach
Part of the Probability Theory and Stochastic Modelling book series (PTSM, volume 91)


Consider some renewal sequence, that is, a sequence of partial sums {Sn}n≥0 of independent identically distributed random variables {Xn}n≥1. Our aim in this chapter is to show that various functionals of partial sums and corresponding renewal processes are asymptotically equivalent if one considers them from the point of view of generalized renewal processes.


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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Valeriĭ V. Buldygin
    • 1
  • Karl-Heinz Indlekofer
    • 2
  • Oleg I. Klesov
    • 3
  • Josef G. Steinebach
    • 4
  1. 1.Department of Mathematical AnalysisNational Technical University of UkraineKyivUkraine
  2. 2.Department of MathematicsUniversity of PaderbornPaderbornGermany
  3. 3.Department of Mathematical Analysis and Probability TheoryNational Technical University of UkraineKyivUkraine
  4. 4.Mathematical InstituteUniversity of CologneCologneGermany

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