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Joint cumulants for natural independence

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	Joint cumulants for natural independence
2.	Creator	Author's name, affiliation, country	Takahiro Hasebe; Kyoto University
2.	Creator	Author's name, affiliation, country	Hayato Saigo; Nagahama Institute of Bio-Science and Technology
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	Natural independence, cumulants, non-commutative probability, monotone independence
3.	Subject	Subject classification	46L53; 46L54; 05A18
4.	Description	Abstract	Many kinds of independence have been defined in non-commutative probability theory. Natural independence is an important class of independence; this class consists of five independences (tensor, free, Boolean, monotone and anti-monotone ones). In the present paper, a unified treatment of joint cumulants is introduced for natural independence. The way we define joint cumulants enables us not only to find the monotone joint cumulants but also to give a new characterization of joint cumulants for other kinds of natural independence, i.e., tensor, free and Boolean independences. We also investigate relations between generating functions of moments and monotone cumulants. We find a natural extension of the Muraki formula, which describes the sum of monotone independent random variables, to the multivariate case.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)	Japan Society for the Promotion of Science
7.	Date	(YYYY-MM-DD)	2011-09-05
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ecp.ejpecp.org/article/view/1647
10.	Identifier	Digital Object Identifier	10.1214/ECP.v16-1647
11.	Source	Journal/conference title; vol., no. (year)	Electronic Communications in Probability; Vol 16
12.	Language	English=en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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