Runs in $m$-Dependent Sequences
Janson, Svante
Ann. Probab., Tome 12 (1984) no. 4, p. 805-818 / Harvested from Project Euclid
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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.
Publié le : 1984-08-14
Classification:  Runs,  $m$-dependent sequences,  random permutations,  60K99,  60G99,  60K05,  60F05,  60C05 
@article{1176993229,
     author = {Janson, Svante},
     title = {Runs in $m$-Dependent Sequences},
     journal = {Ann. Probab.},
     volume = {12},
     number = {4},
     year = {1984},
     pages = { 805-818},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176993229}
}

Janson, Svante. Runs in $m$-Dependent Sequences. Ann. Probab., Tome 12 (1984) no. 4, pp.  805-818. http://gdmltest.u-ga.fr/item/1176993229/