Asymptotic properties of extremal Markov chains of Kendall type. (arXiv:1901.05698v1 [math.PR])

We consider a class of max-AR(1) sequences connected with the Kendall convolution. For a large class of step size distributions we prove that the one dimensional distributions of the Kendall random walk with any unit step distribution, are regularly varying. The finite dimensional distributions for Kendall convolutions are given. We prove convergence of a continuous time stochastic process constructed from the Kendall random walk in the finite dimensional distributions sense using regularly varying functions. 查看全文>>