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Detecting a Local Perturbation in a Continuous Scenery


 
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1. Title Title of document Detecting a Local Perturbation in a Continuous Scenery
 
2. Creator Author's name, affiliation, country Heinrich Matzinger; Georgia Institute of Technology
 
2. Creator Author's name, affiliation, country Serguei Popov; Universidade de São Paulo
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Brownian motion, Poisson process, localization test, detecting defects in sceneries seen along random walks
 
3. Subject Subject classification 60J65, 60K37
 
4. Description Abstract A continuous one-dimensional scenery is a double-infinite sequence of points (thought of as locations of bells) in $R$. Assume that a scenery $X$ is observed along the path of a Brownian motion in the following way: when the Brownian motion encounters a bell different from the last one visited, we hear a ring. The trajectory of the Brownian motion is unknown, whilst the scenery $X$ is known except in some finite interval. We prove that given only the sequence of times of rings, we can a.s. reconstruct the scenery $X$ entirely. For this we take the scenery$X$ to be a local perturbation of a Poisson scenery $X'$. We present an explicit reconstruction algorithm. This problem is the continuous analog of the "detection of a defect in a discrete scenery". Many of the essential techniques used with discrete sceneries do not work with continuous sceneries.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) SFB, CNPq
 
7. Date (YYYY-MM-DD) 2007-05-13
 
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/409
 
10. Identifier Digital Object Identifier 10.1214/EJP.v12-409
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 12
 
12. Language English=en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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