## Electronic Communications in Probability

### Self-averaging sequences which fail to converge

#### 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.

#### Article information

Source
Electron. Commun. Probab., Volume 22 (2017), paper no. 16, 12 pp.

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

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1487386904

Digital Object Identifier
doi:10.1214/17-ECP48

Mathematical Reviews number (MathSciNet)
MR3615667

Zentralblatt MATH identifier
1362.60034

Subjects
Primary: 60F99: None of the above, but in this section

#### Citation

Cator, Eric; Don, Henk. Self-averaging sequences which fail to converge. Electron. Commun. Probab. 22 (2017), paper no. 16, 12 pp. doi:10.1214/17-ECP48. https://projecteuclid.org/euclid.ecp/1487386904

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