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August, 1984 Runs in $m$-Dependent Sequences
Svante Janson
Ann. Probab. 12(3): 805-818 (August, 1984). DOI: 10.1214/aop/1176993229

Abstract

Consider a stationary $m$-dependent sequence of random indicator variables. If $m > 1$, assume further that any two nonzero values are separated by at least $m - 1$ zeros. This paper studies the sequence of the lengths of the successive intervals between the nonzero values of the original sequence, and it is shown that, provided a technical condition holds, these lengths converge in distribution (and their moments converge exponentially fast) in all cases but one.

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Svante Janson. "Runs in $m$-Dependent Sequences." Ann. Probab. 12 (3) 805 - 818, August, 1984. https://doi.org/10.1214/aop/1176993229

Information

Published: August, 1984
First available in Project Euclid: 19 April 2007

zbMATH: 0545.60080
MathSciNet: MR744235
Digital Object Identifier: 10.1214/aop/1176993229

Subjects:
Primary: 60K99
Secondary: 60C05, 60F05, 60G99, 60K05

Rights: Copyright © 1984 Institute of Mathematical Statistics

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Vol.12 • No. 3 • August, 1984
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