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ON DEGENERATE SUMS OF m-DEPENDENT VARIABLES
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
2015 (English)In: Journal of Applied Probability, ISSN 0021-9002, E-ISSN 1475-6072, Vol. 52, no 4, 1146-1155 p.Article in journal (Refereed) Published
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Abstract [en]

It is well known that the central limit theorem holds for partial sums of a stationary sequence (X-i) of m-dependent random variables with finite variance; however, the limit may be degenerate with variance 0 even if var(X-i) not equal 0. We show that this happens only in the case when X-i - EXi = Y-i - Y-i for an (m - 1)-dependent stationary sequence (Y-i) with finite variance (a result implicit in earlier results), and give a version for block factors. This yields a simple criterion that is a sufficient condition for the limit not to be degenerate. Two applications to subtree counts in random trees are given.

Place, publisher, year, edition, pages
2015. Vol. 52, no 4, 1146-1155 p.
Keyword [en]
m-dependent, stationary sequence, block factor, random tree
National Category
Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-277888ISI: 000368467600016OAI: oai:DiVA.org:uu-277888DiVA: diva2:907002
Funder
Knut and Alice Wallenberg Foundation
Available from: 2016-02-25 Created: 2016-02-23 Last updated: 2017-11-30Bibliographically approved

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Janson, Svante

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