Random scaling and sampling of Brownian motion

Mathieu Rosenbaum; Marc Yor

doi:10.2969/jmsj/06741771

Journal of the Mathematical Society of Japan

Online ISSN : 1881-1167
Print ISSN : 0025-5645
ISSN-L : 0025-5645

Random scaling and sampling of Brownian motion

Mathieu Rosenbaum, Marc Yor

著者情報

キーワード: Brownian motion, random scaling, local times, hitting times, uniform sampling, Brownian bridge, Brownian meander, pseudo-Brownian bridge, Bessel process, Ray–Knight theorems, bang-bang process

ジャーナルフリー

2015 年 67 巻 4 号 p. 1771-1784

DOI https://doi.org/10.2969/jmsj/06741771

詳細

抄録

In this paper, we provide a survey of recent distributional results obtained for Brownian type processes observed up to some random times. We focus on the case of hitting times and inverse local times and consider the situation where the processes are randomly sampled through a uniform random variable. We present various explicit formulas, some of them being quite remarkable.