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Filtered Azéma martingales


 
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1. Title Title of document Filtered Azéma martingales
 
2. Creator Author's name, affiliation, country Umut Çetin; London School of Economics and Political Science; United Kingdom
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Azéma's martingale; excursions of Brownian motion; skew Brownian motion; optional projection; local times
 
3. Subject Subject classification 60G35; 60J55; 60H10
 
4. Description Abstract We study the optional projection of a standard Brownian motion on the natural filtration of certain kinds of observation processes. The observation process, $Y$, is defined as a solution of a stochastic differential equation such that it reveals some (possibly noisy) information about the signs of the Brownian motion when $Y$ hits $0$. As such, the associated optional projections are related to Azéma's martingales which are obtained by projecting the Brownian motion onto the filtration generated by observing its signs.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s)
 
7. Date (YYYY-MM-DD) 2012-12-18
 
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/2310
 
10. Identifier Digital Object Identifier 10.1214/ECP.v17-2310
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 17
 
12. Language English=en en
 
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