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Martingales on Random Sets and the Strong Martingale Property


 
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1. Title Title of document Martingales on Random Sets and the Strong Martingale Property
 
2. Creator Author's name, affiliation, country Michael J. Sharpe; University of California, San Diego
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Martingale, random set, strong martingale property
 
3. Subject Subject classification 60J30
 
4. Description Abstract Let $X$ be a process defined on an optional random set. The paper develops two different conditions on $X$ guaranteeing that it is the restriction of a uniformly integrable martingale. In each case, it is supposed that $X$ is the restriction of some special semimartingale $Z$ with canonical decomposition $Z=M+A$. The first condition, which is both necessary and sufficient, is an absolute continuity condition on $A$. Under additional hypotheses, the existence of a martingale extension can be characterized by a strong martingale property of $X$. Uniqueness of the extension is also considered.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s)
 
7. Date (YYYY-MM-DD) 1999-12-16
 
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/57
 
10. Identifier Digital Object Identifier 10.1214/EJP.v5-57
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 5
 
12. Language English=en
 
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