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Localization for controlled random walks and martingales


 
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1. Title Title of document Localization for controlled random walks and martingales
 
2. Creator Author's name, affiliation, country Ori Gurel-Gurevich; None
 
2. Creator Author's name, affiliation, country Yuval Peres; Microsoft Research; United States
 
2. Creator Author's name, affiliation, country Ofer Zeitouni; Weizmann Institute; Israel
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Controlled random walks; Martingales
 
4. Description Abstract We consider controlled random walks that are martingales with uniformly bounded increments and nontrivial  jump probabilities and show that  such walks can be constructed so that $P(S_n^u=0)$ decays at polynomial rate $n^{-\alpha}$ where $\alpha>0$ can be arbitrarily small. We also show, by means of a general delocalization lemma for martingales, which is of independent interest, that slower than polynomial decay is not possible.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s)
 
7. Date (YYYY-MM-DD) 2014-04-26
 
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/3081
 
10. Identifier Digital Object Identifier 10.1214/ECP.v19-3081
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 19
 
12. Language English=en en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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