Unimodality for free Levy processes

Hasebe, Takahiro; Sakuma, Noriyoshi

Annales de l'I.H.P. Probabilités et statistiques, 2017, 53(2), 916-936

Permalink : https://hdl.handle.net/2115/66291

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アクセス権	open access
URI	https://hdl.handle.net/2115/66291
タイトル	Unimodality for free Levy processes
著者	e-Rad_Researcher 00633166 著者名 Hasebe, Takahiro
著者	著者名 Sakuma, Noriyoshi
言語	英語
キーワード	Free probability
	Free convolution
	Free Levy process
	Unimodality
発行日	2017-05
出版者	Institute of Mathematical Statistics
収録物名	Annales de l'I.H.P. Probabilités et statistiques
巻(号)	53(2)
ページ	916-936
抄録	We will prove that: (1) A symmetric free Levy process is unimodal if and only if its free Levy measure is unimodal; (2) Every free Levy process with boundedly supported Levy measure is unimodal in sufficiently large time. (2) is completely different property from classical Levy processes. On the other hand, we find a free Levy process such that its marginal distribution is not unimodal for any time s > 0 and its free Levy measure does not have a bounded support. Therefore, we conclude that the boundedness of the support of free Levy measure in (2) cannot be dropped. For the proof we will (almost) characterize the existence of atoms and the existence of continuous probability densities of marginal distributions of a free Levy process in terms of Levy-Khintchine representation.
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/10.1214/16-AIHP742