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The probability law of the Brownian motion normalized by its range


 
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1. Title Title of document The probability law of the Brownian motion normalized by its range
 
2. Creator Author's name, affiliation, country Florin Spinu; OMERS Capital Markets; Canada
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Brownian motion, Hurwitz zeta
 
3. Subject Subject classification 60J65
 
4. Description Abstract

In the present paper we deduce explicit formulas for the probability laws of the quotients $X_t/R_t$ and $m_t/R_t$, where $X_t$ is the standard Brownian motion and $m_t$, $M_t$, $R_t$ are its running minimum, maximum and range, respectively.The computation makes use of standard techniques from analytic number theory and the theory of the Hurwitz zeta function.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s)
 
7. Date (YYYY-MM-DD) 2013-06-13
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ecp.ejpecp.org/article/view/2568
 
10. Identifier Digital Object Identifier 10.1214/ECP.v18-2568
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 18
 
12. Language English=en en
 
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