Runs in $m$-Dependent Sequences

Svante Janson

doi:10.1214/aop/1176993229

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Home > Journals > Ann. Probab. > Volume 12 > Issue 3 > Article

August, 1984 Runs in $m$-Dependent Sequences

Svante Janson

Ann. Probab. 12(3): 805-818 (August, 1984). DOI: 10.1214/aop/1176993229

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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.