Asymptotic Properties of Extremal Markov Processes Driven by Kendall Convolution

Abstract

This paper is devoted to the analysis of the finite-dimensional distributions and asymptotic behavior of extremal Markov processes connected with the Kendall convolution. In particular, we provide general formulas for the finite dimensional distributions of the random walk driven by the Kendall convolution for a large class of step size distributions. Moreover, we prove limit theorems for random walks and associated continuous-time stochastic processes.