Self-averaging sequences which fail to converge [article]

Eric Cator, Henk Don
2016 arXiv   pre-print
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 nth 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.
arXiv:1609.07971v2 fatcat:35fu6cz7encxld265wkfzoard4