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2009 A Log-Type Moment Result for Perpetuities and Its Application to Martingales in Supercritical Branching Random Walks
Gerold Alsmeyer, Alex Iksanov
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Electron. J. Probab. 14: 289-313 (2009). DOI: 10.1214/EJP.v14-596

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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Gerold Alsmeyer. Alex Iksanov. "A Log-Type Moment Result for Perpetuities and Its Application to Martingales in Supercritical Branching Random Walks." Electron. J. Probab. 14 289 - 313, 2009. https://doi.org/10.1214/EJP.v14-596

Information

Accepted: 29 January 2009; Published: 2009
First available in Project Euclid: 1 June 2016

zbMATH: 1191.60098
MathSciNet: MR2471666
Digital Object Identifier: 10.1214/EJP.v14-596

Subjects:
Primary: 60G42, 60J80
Secondary: 60K05

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