文章基本信息

标题：Large time unimodality for classical and free Brownian motions with initial distributions
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作者：Takahiro Hasebe ; Yuki Ueda
期刊名称：Latin American Journal of Probability and Mathematical Statistics
电子版ISSN：1980-0436
出版年度：2018
卷号：XV
期号：1
页码：353-374
DOI：10.30757/ALEA.v15-15
出版社：Instituto Nacional De Matemática Pura E Aplicada
摘要：We prove that classical and free Brownian motions with initial distri-butions are unimodal for sufficiently large time, under some assumption on theinitial distributions. The assumption is almost optimal in some sense. Similar re-sults are shown for a symmetric stable process with index 1 and a positive stableprocess with index 1/2. We also prove that free Brownian motion with initial sym-metric unimodal distribution is unimodal, and discuss strong unimodality for freeconvolution.
关键词：unimodal; strongly unimodal; Brownian motion; Cauchy process;positive stable process;