Open Access
October, 2015 Random scaling and sampling of Brownian motion
J. Math. Soc. Japan 67(4): 1771-1784 (October, 2015). DOI: 10.2969/jmsj/06741771


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.


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Mathieu ROSENBAUM. Marc YOR. "Random scaling and sampling of Brownian motion." J. Math. Soc. Japan 67 (4) 1771 - 1784, October, 2015.


Published: October, 2015
First available in Project Euclid: 27 October 2015

zbMATH: 1335.60157
MathSciNet: MR3417513
Digital Object Identifier: 10.2969/jmsj/06741771

Primary: 60G40 , 60J65
Secondary: 60G17 , 60J55

Keywords: bang-bang process , Bessel process , Brownian bridge , Brownian meander , Brownian motion , hitting times , Local times , pseudo-Brownian bridge , random scaling , Ray–Knight theorems , uniform sampling

Rights: Copyright © 2015 Mathematical Society of Japan

Vol.67 • No. 4 • October, 2015
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