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arXiv · 1609.07971

Self-averaging sequences which fail to converge

Eric Cator·Henk Don
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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.

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Eric Cator, Henk Don. 2016-09-26. Self-averaging sequences which fail to converge. https://arxiv.org/abs/1609.07971

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