2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/117848We 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.Published at http://dx.doi.org/10.1214/105051606000000321 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)Probability60G70 (Primary) 60F10 (Secondary)text