On the length of the longest run in a multi-state Markov chain

Vaggelatou, E

dc.contributor.author	Vaggelatou, E	en
dc.date.accessioned	2014-03-01T01:19:22Z
dc.date.available	2014-03-01T01:19:22Z
dc.date.issued	2003	en
dc.identifier.issn	0167-7152	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/15449
dc.subject	Erdös-Renyi type law	en
dc.subject	Extreme value distribution	en
dc.subject	Longest run	en
dc.subject	Multi-state trials	en
dc.subject.classification	Statistics & Probability	en
dc.subject.other	PATTERNS	en
dc.subject.other	SEQUENCE	en
dc.title	On the length of the longest run in a multi-state Markov chain	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/S0167-7152(02)00432-7	en
heal.identifier.secondary	http://dx.doi.org/10.1016/S0167-7152(02)00432-7	en
heal.language	English	en
heal.publicationDate	2003	en
heal.abstract	Let {X-a}(ais an element ofz) be an irreducible and aperiodic Markov chain on a finite state space S = {0, 1,...,r}, r greater than or equal to 1. Denote by L-n the length of the longest run of consecutive i's, for i = that occurs in the sequence X-1,...,X-n. In this work, we extend a result of Goncharov (Amer. Math. Soc. Transl. 19 (1943) 1) which concerned a limit law for L-n in sequences of 0-1 i.i.d. trials. Moreover, it is shown that L-n has approximately an extreme value distribution along a certain subsequence. Finally, a weak version of an Erdos-Renyi type law for L-n is proved. (C) 2003 Elsevier Science B.V. All rights reserved.	en
heal.publisher	ELSEVIER SCIENCE BV	en
heal.journalName	Statistics and Probability Letters	en
dc.identifier.doi	10.1016/S0167-7152(02)00432-7	en
dc.identifier.isi	ISI:000182152200001	en
dc.identifier.volume	62	en
dc.identifier.issue	3	en
dc.identifier.spage	211	en
dc.identifier.epage	221	en