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2019 A revisited proof of the Seneta-Heyde norming for branching random walks under optimal assumptions
Pierre Boutaud, Pascal Maillard
Electron. J. Probab. 24: 1-22 (2019). DOI: 10.1214/19-EJP350

Abstract

We introduce a set of tools which simplify and streamline the proofs of limit theorems concerning near-critical particles in branching random walks under optimal assumptions. We exemplify our method by giving another proof of the Seneta-Heyde norming for the critical additive martingale, initially due to Aïdékon and Shi. The method involves in particular the replacement of certain second moment estimates by truncated first moment bounds, and the replacement of ballot-type theorems for random walks by estimates coming from an explicit expression for the potential kernel of random walks killed below the origin. Of independent interest might be a short, self-contained proof of this expression, as well as a criterion for convergence in probability of non-negative random variables in terms of conditional Laplace transforms.

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Pierre Boutaud. Pascal Maillard. "A revisited proof of the Seneta-Heyde norming for branching random walks under optimal assumptions." Electron. J. Probab. 24 1 - 22, 2019. https://doi.org/10.1214/19-EJP350

Information

Received: 20 February 2019; Accepted: 5 August 2019; Published: 2019
First available in Project Euclid: 18 September 2019

zbMATH: 07107406
MathSciNet: MR4017117
Digital Object Identifier: 10.1214/19-EJP350

Subjects:
Primary: 60J80
Secondary: 60B10, 60J50

JOURNAL ARTICLE
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Vol.24 • 2019
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