Kendall random walks

• Autorzy: Jasiulis-Gołdyn B. H.
• Języki publikacji: EN

Abstrakty

EN

The paper deals with a new class of random walks strictly connected with the Pareto distribution. We consider stochastic processes in the sense of generalized convolution or weak generalized convolution. The processes are Markov processes in the usual sense. Their structure is similar to perpetuity or autoregressive model. We prove the theorem which describes the magnitude of the fluctuations of random walks generated by generalized convolutions. We give a construction and basic properties of random walks with respect to the Kendall convolution.We show that they are not classical Lévy processes. The paper proposes a new technique to cumulate the Pareto-type distributions using a modification of the Williamson transform and contains many new properties of weakly stable probability measure connected with the Kendall convolution. It seems that the Kendall convolution produces a new class of heavy tailed distributions of Pareto-type.

Słowa kluczowe

EN

random walk; generalized convolution; weakly stable distribution; Kendall convolution; Pareto distribution; Markov process; Williamson transform

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2016
• Tom: Vol. 36, Fasc. 1
• Strony: 165--185
• Opis fizyczny: Bibliogr. 24 poz.

Twórcy

autor

Jasiulis-Gołdyn B. H.

• Institute of Mathematics, Wrocław University, pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland

Bibliografia

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• [6] B. H. Jasiulis, Limit property for regular and weak generalized convolutions, J. Theoret. Probab. 23 (1) (2010), pp. 315-327.
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• [8] B. H. Jasiulis-Gołdyn and J. K. Misiewicz, On the uniqueness of the Kendall generalized convolution, J. Theoret. Probab. 24 (3) (2011), pp. 746-755.
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Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).