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A Log-Type Moment Result for Perpetuities and Its Application to Martingales in Supercritical Branching Random Walks


 
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1. Title Title of document A Log-Type Moment Result for Perpetuities and Its Application to Martingales in Supercritical Branching Random Walks
 
2. Creator Author's name, affiliation, country Gerold Alsmeyer; Institut fur Mathematische Statistik, Munster University
 
2. Creator Author's name, affiliation, country Alex Iksanov; Faculty of Cybernetics, National T.Shevchenko University of Kiev
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) branching random walk; martingale; moments; perpetuity
 
3. Subject Subject classification Primary 60J80, 60G42; Secondary 60K05
 
4. Description Abstract Infinite sums of i.i.d. random variables discounted by a multiplicative random walk are called perpetuities and have been studied by many authors. The present paper provides a log-type moment result for such random variables under minimal conditions which is then utilized for the study of related moments of a.s. limits of certain martingales associated with the supercritical branching random walk. The connection arises upon consideration of a size-biased version of the branching random walk originally introduced by Lyons. As a by-product, necessary and sufficient conditions for uniform integrability of these martingales are provided in the most general situation which particularly means that the classical (LlogL)-condition is not always needed.
 
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6. Contributor Sponsor(s)
 
7. Date (YYYY-MM-DD) 2009-01-29
 
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/596
 
10. Identifier Digital Object Identifier 10.1214/EJP.v14-596
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 14
 
12. Language English=en
 
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