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A maximal inequality for supermartingales


 
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1. Title Title of document A maximal inequality for supermartingales
 
2. Creator Author's name, affiliation, country Bruce Hajek; University of Illinois at Urbana-Champaign; United States
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) maximal inequality; semimartingale calculus; drift; martingale
 
3. Subject Subject classification 60G40;93E20;60G42;60G44
 
4. Description Abstract A tight upper bound is given on the distribution of the maximum of a supermartingale. Specifically, it is shown that if $Y$ is a semimartingale with initial value zero and quadratic variation process $[Y,Y]$ such that $Y + [Y,Y]$ is a supermartingale, then the probability the maximum of $Y$ is greater than or equal to a positive constant $a$ is less than or equal to$1/(1+a).$ The proof makes use of the semimartingale calculus and is inspired by dynamic programming.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) National Science Foundation
 
7. Date (YYYY-MM-DD) 2014-08-14
 
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/3237
 
10. Identifier Digital Object Identifier 10.1214/ECP.v19-3237
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 19
 
12. Language English=en en
 
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