自由卷积和布尔卷积对Cauchy-Stieltjes核族影响的研究

IF 1.3 Q2 STATISTICS & PROBABILITY Probability Surveys Pub Date : 2022-01-01 DOI:10.1214/22-ps10
Raouf Fakhfakh
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引用次数: 2

摘要

在非对易概率论的背景下,与自然指数族理论相类似,最近引入了Cauchy-Stieltjes核族理论。它基于Cauchy-Stieltjes核(1−θx)−1。在本文中,在介绍了NEFs和CSK族的一些基本概念并指出了这两个族之间的一些异同之后,我们回顾了自由卷积幂和布尔卷积幂对CSK族影响的现状和发展。MSC2020受试者分类:60E10、46L54。
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A survey on the effects of free and boolean convolutions on Cauchy-Stieltjes Kernel families
In the setting of noncommutative probability theory and in analogy with the theory of natural exponential families (NEFs), a theory of Cauchy-Stieltjes Kernel (CSK) families has been recently introduced. It is based on the Cauchy-Stieltjes kernel (1 − θx)−1. In this paper, after presenting some basic concepts on NEFs and CSK families and pointing out some similarities and differences between the two families, we review the present state and developments regarding the effects of free and boolean convolutions powers on CSK families. MSC2020 subject classifications: 60E10, 46L54.
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来源期刊
Probability Surveys
Probability Surveys STATISTICS & PROBABILITY-
CiteScore
4.70
自引率
0.00%
发文量
9
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