Annals of Applied Probability

Local alignment of Markov chains

Niels Richard Hansen

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We consider local alignments without gaps of two independent Markov chains from a finite alphabet, and we derive sufficient conditions for the number of essentially different local alignments with a score exceeding a high threshold to be asymptotically Poisson distributed. From the Poisson approximation a Gumbel approximation of the maximal local alignment score is obtained. The results extend those obtained by Dembo, Karlin and Zeitouni [Ann. Probab. 22 (1994) 2022–2039] for independent sequences of i.i.d. variables.

Article information

Ann. Appl. Probab., Volume 16, Number 3 (2006), 1262-1296.

First available in Project Euclid: 2 October 2006

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60G70: Extreme value theory; extremal processes
Secondary: 60F10: Large deviations

Chen–Stein method extreme value theory large deviations local alignment Markov additive processes Markov chains Poisson approximation


Hansen, Niels Richard. Local alignment of Markov chains. Ann. Appl. Probab. 16 (2006), no. 3, 1262--1296. doi:10.1214/105051606000000321.

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