论文标题
自由偶发性的对数 - 抑制性
Log-unimodality for free positive multiplicative Brownian motion
论文作者
论文摘要
我们证明，边际定律$σ_{t} \boxtimesν$免费的乘数布朗运动是所有$ t> 0 $的log inmodal，如果$ν$是一种多上对称的对数 - 单数分布，则$σ_{t} {t} \ boxtimes的$ iS $ to $ unimodal $ t $ t $ t $ t $ t $ t $ t $ t $ t $ t $ t $ t $ t $ T 间隔。当$ν$不假定对称或有界支持时，给出反例。
We prove that the marginal law $σ_{t}\boxtimesν$ of free positive multiplicative Brownian motion is log-unimodal for all $t>0$ if $ν$ is a multiplicatively symmetric log-unimodal distribution, and that $σ_{t}\boxtimesν$ is log-unimodal for sufficiently large $t$ if $ν$ is supported on a suitably chosen finite interval. Counterexamples are given when $ν$ is not assumed to be symmetric or having a bounded support.
