Limit Theorems for Classical, Freely and Boolean Max-Infinitely Divisible Distributions

Yuki Ueda ()
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Yuki Ueda: Hokkaido University

Journal of Theoretical Probability, 2022, vol. 35, issue 1, 89-114

Abstract: Abstract We investigate a Belinschi–Nica-type semigroup for free and Boolean max-convolutions. We prove that this semigroup at time one connects limit theorems for freely and Boolean max-infinitely divisible distributions. Moreover, we also construct a max-analogue of Boolean-classical Bercovici–Pata bijection, establishing the equivalence of limit theorems for Boolean and classical max-infinitely divisible distributions.

Keywords: Max-convolution; Max-stable (extreme value) distributions; Max-infinitely divisible distributions; Max-Belinschi–Nica semigroup; Max-compound Poisson distributions; 46L54; 60E07; 60G70 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10959-020-01060-7

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