Fluctuations of extremal Markov chains of the Kendall type

The paper deals with fluctuations of Kendall random walks, which are extremal Markov chains. We give the joint distribution of the first ascending ladder epoch and height over any level $a geq 0$ and distribution of maximum and minimum for these extremal Markovian sequences. We show that distribution of the first crossing time of level $a geq0$ is a mixture of geometric and negative binomial distributions. The Williamson transform is the main tool for considered problems connected with the Kendall convolution.