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Limit Theorems for Classical, Freely and Boolean Max-Infinitely Divisible Distributions
Journal of Theoretical Probability ( IF 0.8 ) Pub Date : 2021-01-02 , DOI: 10.1007/s10959-020-01060-7
Yuki Ueda

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.

中文翻译:

经典、自由和布尔最大无限可分分布的极限定理

我们研究了自由和布尔最大卷积的 Belinschi-Nica 型半群。我们证明这个半群在时间 1 连接了自由分布和布尔最大无限可分分布的极限定理。此外,我们还构建了布尔经典 Bercovici-Pata 双射的最大模拟,建立了布尔和经典最大无限可分分布的极限定理的等价性。
更新日期:2021-01-02
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