Journal of the Mathematical Society of Japan

Random scaling and sampling of Brownian motion

Mathieu ROSENBAUM and Marc YOR

Full-text: Open access

Abstract

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

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

Dates
First available in Project Euclid: 27 October 2015

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1445951166

Digital Object Identifier
doi:10.2969/jmsj/06741771

Mathematical Reviews number (MathSciNet)
MR3417513

Zentralblatt MATH identifier
1335.60157

Subjects
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

Keywords
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

Citation

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. https://projecteuclid.org/euclid.jmsj/1445951166


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References

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