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Renewal theory for extremal Markov sequences of Kendall type

Author

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  • Jasiulis-Gołdyn, Barbara H.
  • Misiewicz, Jolanta K.
  • Naskręt, Karolina
  • Omey, Edward

Abstract

The paper deals with renewal theory for a class of extremal Markov sequences connected with the Kendall convolution. We consider here some particular cases of the Wold processes associated with generalized convolutions. We prove an analogue of the Fredholm theorem for all regular generalized convolutions algebras. Using regularly varying functions we prove a Blackwell theorem and a limit theorem for renewal processes defined by Kendall random walks.

Suggested Citation

  • Jasiulis-Gołdyn, Barbara H. & Misiewicz, Jolanta K. & Naskręt, Karolina & Omey, Edward, 2020. "Renewal theory for extremal Markov sequences of Kendall type," Stochastic Processes and their Applications, Elsevier, vol. 130(6), pages 3277-3294.
    • Handle: RePEc:eee:spapps:v:130:y:2020:i:6:p:3277-3294
    DOI: 10.1016/j.spa.2019.09.013
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    Cited by:

    1. M. Arendarczyk & T. J. Kozubowski & A. K. Panorska, 2023. "Slash distributions, generalized convolutions, and extremes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 75(4), pages 593-617, August.

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