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Unimodality for free Levy processes

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タイトル: Unimodality for free Levy processes
著者: Hasebe, Takahiro 著作を一覧する
Sakuma, Noriyoshi 著作を一覧する
キーワード: Free probability
Free convolution
Free Levy process
Unimodality
発行日: 2017年 5月
出版者: Institute of Mathematical Statistics
誌名: Annales de l'I.H.P. Probabilités et statistiques
巻: 53
号: 2
開始ページ: 916
終了ページ: 936
出版社 DOI: 10.1214/16-AIHP742
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.
資料タイプ: article
URI: http://hdl.handle.net/2115/66291
出現コレクション:雑誌発表論文等 (Peer-reviewed Journal Articles, etc)

提供者: 長谷部 高広

 

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