Exact distribution for the local score of a Markov chain.

Given a sequence X = (X-k)(kgreater than or equal to1) of random variables taking values in {-nu,...,0,..., +u}, let's define the local score of the sequence by H-n = max(1less than or equal toiless than or equal tojless than or equal ton)(Sigma(k=i)(j) X-k). The local score is used to analyze biological sequences pointing out regions of the sequences with interesting biological properties. In order to separate randomly events from really interesting segments, we establish here the distribution of the local score of H-n when the sequence X is a Markov chain of order 1. (C) 2003 Academie des sciences. Publie par Editions scientifiques et medicales Elsevier SAS. Tous droits reserves.