Fluctuations of extremal Markov chains of the Kendall type

Published in Arxiv preprint, 2019

Abstract: 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 >= 0 and distribution of maximum and minimum for these extremal Markovian sequences. We show that distribution of the first crossing time of level a > 0 is a mixture of geometric and negative binomial distributions. The Williamson transform is the main tool for considered problems connected with the Kendall convolution.

Recommended citation: B.H. Jasiulis-Gołdyn, M. Staniak, "Fluctuations of extremal Markov chains of the Kendall type", arxiv e-print, 2019.