Annals of Applied Probability

Local alignment of Markov chains

Niels Richard Hansen

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Abstract

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

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

Dates
First available in Project Euclid: 2 October 2006

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1159804981

Digital Object Identifier
doi:10.1214/105051606000000321

Mathematical Reviews number (MathSciNet)
MR2260063

Zentralblatt MATH identifier
1113.60054

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

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

Citation

Hansen, Niels Richard. Local alignment of Markov chains. Ann. Appl. Probab. 16 (2006), no. 3, 1262--1296. doi:10.1214/105051606000000321. https://projecteuclid.org/euclid.aoap/1159804981


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