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Renewal theory for extremal Markov sequences of Kendall type

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. Our results set new research hypotheses for other generalized convolution algebras to investigate renewal processes constructed by Markov processes with respect to generalized convolutions.