# Fluctuations of extremal Markov chains driven by the Kendall convolution

@inproceedings{JasiulisGodyn2019FluctuationsOE, title={Fluctuations of extremal Markov chains driven by the Kendall convolution}, author={Barbara H. Jasiulis-Gołdyn and Edward Omey and Mateusz Staniak}, year={2019} }

. The paper deals with ﬂuctuations of Kendall random walks, which are extremal Markov chains and iterated integral transforms with the Williamson kernel Ψ( t ) = (1 − | t | α ) + , α > 0. We obtain the joint distribution of the ﬁrst ascending ladder epoch and height over any level a 0 and distribution of maximum and minimum for these extremal Markovian sequences solving recursive integral equations. We show that distribution of the ﬁrst crossing time of level a 0 is a mixture of geometric and…

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