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

Eutichia Vaggelatou

Statistics & Probability Letters, 2003, vol. 62, issue 3, 211-221

Abstract: Let {Xa}a[set membership, variant]Z be an irreducible and aperiodic Markov chain on a finite state space S={0,1,...,r}, r[greater-or-equal, slanted]1. Denote by Ln the length of the longest run of consecutive i's, for i=1,...,r, that occurs in the sequence X1,...,Xn. In this work, we extend a result of Goncharov (Amer. Math. Soc. Transl. 19 (1943) 1) which concerned a limit law for Ln in sequences of 0-1 i.i.d. trials. Moreover, it is shown that Ln has approximately an extreme value distribution along a certain subsequence. Finally, a weak version of an Erdös-Rényi type law for Ln is proved.

Keywords: Longest; run; Multi-state; trials; Extreme; value; distribution; Erdös-Rényi; type; law (search for similar items in EconPapers)
Date: 2003
References: View complete reference list from CitEc
Citations: View citations in EconPapers (5)

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