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December 2015 On degenerate sums of m-dependent variables
Svante Janson
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J. Appl. Probab. 52(4): 1146-1155 (December 2015). DOI: 10.1239/jap/1450802758

Abstract

It is well known that the central limit theorem holds for partial sums of a stationary sequence (Xi) of m-dependent random variables with finite variance; however, the limit may be degenerate with variance 0 even if var(Xi) ≠ 0. We show that this happens only in the case when Xi - EXi = Yi - Yi-1 for an (m - 1)-dependent stationary sequence (Yi) 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.

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Svante Janson. "On degenerate sums of m-dependent variables." J. Appl. Probab. 52 (4) 1146 - 1155, December 2015. https://doi.org/10.1239/jap/1450802758

Information

Published: December 2015
First available in Project Euclid: 22 December 2015

zbMATH: 1334.60021
MathSciNet: MR3439177
Digital Object Identifier: 10.1239/jap/1450802758

Subjects:
Primary: 60G10
Secondary: 60C05, 60F05

Rights: Copyright © 2015 Applied Probability Trust

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Vol.52 • No. 4 • December 2015
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