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On convergence of randomly indexed sequences; a counterexample based on the St. Petersburg game
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
2014 (English)In: Statistics and Probability Letters, ISSN 0167-7152, E-ISSN 1879-2103, Vol. 87, 105-107 p.Article in journal (Refereed) Published
Abstract [en]

If Y-1, Y-2,... is a sequence of random variables such that Y-n -> Y as n -> infinity, and {tau(t), t >= 0} is a family of "indices" such that tau(t) -> infinity t -> infinity, then it is pretty obvious that Y-tau(t) -> Y as t -> infinity. However, if one relaxes one of -> to -> and lets the other one remain as is, then one of the resulting conclusions holds, whereas the other one does not. In this note we provide a "more natural" counterexample than the original one due to Richter (1965), followed by a minor extension.

Place, publisher, year, edition, pages
2014. Vol. 87, 105-107 p.
Keyword [en]
Random index, St. Petersburg game, Sums of i.i.d. random variables
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:uu:diva-224914DOI: 10.1016/j.spl.2014.01.011ISI: 000334486200016OAI: oai:DiVA.org:uu-224914DiVA: diva2:720268
Available from: 2014-05-28 Created: 2014-05-23 Last updated: 2017-12-05Bibliographically approved

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Gut, Allan

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