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On the expectation of normalized Brownian functionals up to first hitting times


 
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1. Title Title of document On the expectation of normalized Brownian functionals up to first hitting times
 
2. Creator Author's name, affiliation, country Romuald Elie; University Paris-Est Marne-La-Vallée; France
 
2. Creator Author's name, affiliation, country Mathieu Rosenbaum; University Pierre et Marie Curie (Paris 6); France
 
2. Creator Author's name, affiliation, country Marc Yor; University Pierre et Marie Curie; France
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Brownian motion, hitting times, scaling, random sampling, Bessel process, Brownian meander, Ray-Knight theorem, Feynman-Kac formula.
 
3. Subject Subject classification 60J65;60J55;60G40
 
4. Description Abstract Let $B$ be a Brownian motion and $T_1$ its first hitting time of the level $1$. For $U$ a uniform random variable independent of $B$, we study in depth the distribution of $B_{UT_1}/\sqrt{T_1}$, that is the rescaled Brownian motion sampled at uniform time. In particular, we show that this variable is centered.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s)
 
7. Date (YYYY-MM-DD) 2014-03-29
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/3049
 
10. Identifier Digital Object Identifier 10.1214/EJP.v19-3049
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 19
 
12. Language English=en en
 
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