The monotone cumulants

Hasebe, Takahiro; Saigo, Hayato

Annales de l'Institut Henri Poincaré, Probabilités et Statistiques, 2011, 47(4), 1160-1170

Permalink : https://hdl.handle.net/2115/75991

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ファイル	フォーマット	サイズ	閲覧回数	説明
Ann. I.H.P. Probab. stat47-4_1160-1170	pdf	197 KB	370

アクセス権	open access
URI	https://hdl.handle.net/2115/75991
タイトル	The monotone cumulants
著者	e-Rad_Researcher 00633166 著者名 Hasebe, Takahiro
著者	著者名 Saigo, Hayato
言語	英語
キーワード	Monotone independence
	Cumulants
	Umbral calculus
発行日	2011
収録物名	Annales de l'Institut Henri Poincaré, Probabilités et Statistiques
巻(号)	47(4)
ページ	1160-1170
抄録	In the present paper we define the notion of generalized cumulants which gives a universal framework for commutative, free, Boolean and especially, monotone probability theories. The uniqueness of generalized cumulants holds for each independence, and hence, generalized cumulants are equal to the usual cumulants in the commutative, free and Boolean cases. The way we define (generalized) cumulants needs neither partition lattices nor generating functions and then will give a new viewpoint to cumulants. We define “monotone cumulants” in the sense of generalized cumulants and we obtain quite simple proofs of central limit theorem and Poisson’s law of small numbers in monotone probability theory. Moreover, we clarify a combinatorial structure of moment-cumulant formula with the use of “monotone partitions.”
資源タイプ	学術雑誌論文
出版タイプ	Version of Record
PISSN	0246-0203
関連情報 (isIdenticalTo)	出版社版DOI https://doi.org/10.1214/10-AIHP379