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2017 Self-averaging sequences which fail to converge
Eric Cator, Henk Don
Electron. Commun. Probab. 22: 1-12 (2017). DOI: 10.1214/17-ECP48

Abstract

We consider self-averaging sequences in which each term is a weighted average over previous terms. For several sequences of this kind it is known that they do not converge to a limit. These sequences share the property that $n$th term is mainly based on terms around a fixed fraction of $n$. We give a probabilistic interpretation to such sequences and give weak conditions under which it is natural to expect non-convergence. Our methods are illustrated by application to the group Russian roulette problem.

Citation

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Eric Cator. Henk Don. "Self-averaging sequences which fail to converge." Electron. Commun. Probab. 22 1 - 12, 2017. https://doi.org/10.1214/17-ECP48

Information

Received: 3 October 2016; Accepted: 30 January 2017; Published: 2017
First available in Project Euclid: 18 February 2017

zbMATH: 1362.60034
MathSciNet: MR3615667
Digital Object Identifier: 10.1214/17-ECP48

Subjects:
Primary: 60F99

JOURNAL ARTICLE
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