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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, p. 1146-1155Article 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, p. 1146-1155
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, id: 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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