Self-averaging sequences which fail to converge
Self-averaging sequences which fail to converge
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DOI：
10.1214/17-ecp48
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发表时间：
2016-09
期刊：
影响因子：
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通讯作者：
E. Cator;H. Don
中科院分区：
文献类型：
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作者：
E. Cator;H. Don
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.
