Asymptotic Properties of Extremal Markov Processes Driven by Kendall Convolution

Marek Arendarczyk (), Barbara Jasiulis-Gołdyn () and Edward Omey ()
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Marek Arendarczyk: University of Wrocław
Barbara Jasiulis-Gołdyn: University of Wrocław
Edward Omey: KU Leuven

Journal of Theoretical Probability, 2023, vol. 36, issue 4, 2040-2065

Abstract: 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.

Keywords: Markov process; Extremes; Kendall convolution; Regular variation; Williamson transform; Limit theorems; Exact asymptotics; 60G70; 60F05; 44A35; 60J05; 60J35; 60E07; 60E10 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10959-023-01285-2

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