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Conditioned martingales


 
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1. Title Title of document Conditioned martingales
 
2. Creator Author's name, affiliation, country Nicolas Perkowski; Humboldt-Universität zu Berlin; Germany
 
2. Creator Author's name, affiliation, country Johannes Ruf; University of Oxford; United Kingdom
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Doob’s h-transform; change of measure; upward conditioning; downward conditioning; local martingale; diffusion; nullset; Bessel process
 
3. Subject Subject classification 60G44; 60H99; 60J60
 
4. Description Abstract

It is well known that upward conditioned Brownian motion is a three-dimensional Bessel process, and that a downward conditioned Bessel process is a Brownian motion. We give a simple proof for this result, which generalizes to any continuous local martingale and clarifies the role of finite versus infinite time in this setting. As a consequence, we can describe the law of regular diffusions that are conditioned upward or downward.

 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s)
 
7. Date (YYYY-MM-DD) 2012-10-09
 
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/1955
 
10. Identifier Digital Object Identifier 10.1214/ECP.v17-1955
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 17
 
12. Language English=en en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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