Marginal densities of the least concave majorant of Brownian motion

• 成果类型: Article
• 署名作者: Carolan, C; Dykstra, R
• 署名单位: University of North Carolina; East Carolina University; University of Iowa
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 2001
• 页码: 1732-1750
• 关键词: LIKELIHOOD

摘要

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.