Marginal Densities of the Least Concave Majorant of Brownian Motion
Marginal Densities of the Least Concave Majorant of Brownian Motion
复制标题
布朗运动最小凹主函数的边缘密度
DOI：
10.1214/aos/1015345960
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发表时间：
2001
影响因子：
4.5
通讯作者：
R. Dykstra
中科院分区：
文献类型：
--
作者：
C. Carolan;R. Dykstra
布朗运动、其最小凹主函数及其导数都在同一固定点导出了干净、封闭的形式、关节密度。这种联合密度得出一些显着的条件分布和边际分布。例如，表明在固定时间点布朗运动的最小凹主波的高度与在同一固定时间点布朗运动路径到其最小凹主波的距离具有相同的分布。同时还表明，以某一固定时间点布朗运动最小凹主波的高度为条件，同一固定时间点布朗运动最小凹主波的左斜率是均匀分布的。
A clean, closed form, joint density is derived for Brownian motion, its least concave majorant, and its derivative, all at the same fixed point. Some remarkable conditional and marginal distributions follow from this joint density. For example, it is shown that the height of the least concave majorant of Brownian motion at a fixed time point has the same distribution as the distance from the Brownian motion path to its least concave majorant at the same fixed time point. Also, it is shown that conditional on the height of the least concave majorant of Brownian motion at a fixed time point, the left-hand slope of the least concave majorant of Brownian motion at the same fixed time point is uniformly distributed.