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

By Gerold Alsmeyer, Alexander Iksanov. 2008

48 citations recorded by the source corpus.

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.

Subfields: Finance, Management Science and Operations Research, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/96e0b98b6207cdadf91c5ef1be9057d72de44760

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Finance

1. Gerold Alsmeyer
2. Alexander Iksanov

In Management Science and Operations Research

1. Gerold Alsmeyer
2. Alexander Iksanov

In Mathematical Physics

1. Gerold Alsmeyer
2. Uwe Rösler
3. Alexander Iksanov

Citations in the corpus

• On Distributional Properties of Perpetuities (2008, background): “The latter is studied in recent work by the first two authors [1] and is of additional interest due to the connection of perpetuities with certain intrinsic martingales in the supercritical branching random walk.”