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Asymptotic Properties of Extremal Markov Processes Driven by Kendall Convolution

Author

Listed:
  • Marek Arendarczyk

    (University of Wrocław)

  • Barbara Jasiulis-Gołdyn

    (University of Wrocław
    University of Liverpool)

  • Edward Omey

    (KU Leuven)

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.

Suggested Citation

  • Marek Arendarczyk & Barbara Jasiulis-Gołdyn & Edward Omey, 2023. "Asymptotic Properties of Extremal Markov Processes Driven by Kendall Convolution," Journal of Theoretical Probability, Springer, vol. 36(4), pages 2040-2065, December.
    • Handle: RePEc:spr:jotpro:v:36:y:2023:i:4:d:10.1007_s10959-023-01285-2
    DOI: 10.1007/s10959-023-01285-2
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    References listed on IDEAS

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    1. B. H. Jasiulis-Gołdyn & J. K. Misiewicz, 2011. "On the Uniqueness of the Kendall Generalized Convolution," Journal of Theoretical Probability, Springer, vol. 24(3), pages 746-755, September.
    2. Alpuim, M. T. & Catkan, N. A. & Hüsler, J., 1995. "Extremes and clustering of nonstationary max-AR(1) sequences," Stochastic Processes and their Applications, Elsevier, vol. 56(1), pages 171-184, March.
    3. McNeil, Alexander J. & Neslehová, Johanna, 2010. "From Archimedean to Liouville copulas," Journal of Multivariate Analysis, Elsevier, vol. 101(8), pages 1772-1790, September.
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