A Vervaat like path transformation for the reflected Brownian bridge conditioned on its local time at 0

• 成果类型: Article
• 署名作者: Chassaing, P; Janson, S
• 署名单位: Universite de Lorraine; Uppsala University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• 发表日期: 2001
• 页码: 1755-1779
• 关键词: excursion; graphs; coalescent; meander; motion

摘要

We describe a Vervaat-like path transformation for the reflected Brownian bridge conditioned on its local time at 0: up to random shifts, this process equals the two processes constructed from a Brownian bridge and a Brownian excursion by adding a drift and then taking the excursions over the current minimum. As a consequence, these three processes have the same occupation measure, which is easily found. The three processes arise as limits, in three different ways, of profiles associated to hashing with linear probing, or, equivalently, to parking functions.