Renewal theory for extremal Markov sequences of Kendall type

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

Stochastic Processes and their Applications, 2020, vol. 130, issue 6, 3277-3294

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.

Keywords: Kendall random walk; Renewal theory; Regularly varying function; Fredholm theorem; Blackwell theorem; Wold process (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:130:y:2020:i:6:p:3277-3294

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DOI: 10.1016/j.spa.2019.09.013

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