Journal of the Mathematical Society of Japan

Random scaling and sampling of Brownian motion

Mathieu ROSENBAUM and Marc YOR

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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.

Article information

J. Math. Soc. Japan, Volume 67, Number 4 (2015), 1771-1784.

First available in Project Euclid: 27 October 2015

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Zentralblatt MATH identifier

Primary: 60G40: Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60] 60J65: Brownian motion [See also 58J65]
Secondary: 60G17: Sample path properties 60J55: Local time and additive functionals

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


ROSENBAUM, Mathieu; YOR, Marc. Random scaling and sampling of Brownian motion. J. Math. Soc. Japan 67 (2015), no. 4, 1771--1784. doi:10.2969/jmsj/06741771.

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