Distribution exacte du score local,cas markovien

Given a sequence $\text{X}\text{=(X}{}_{\mathrm{k}}\text{)}{}_{\mathrm{k?1}}$ of random variables taking values in {?v,…,0,…,+u}, let's define the local score of the sequence by H_n=max_1?i?j?n(∑_k=i^jX_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 $\text{X}$ is a Markov chain of order 1. To cite this article: S. Mercier, C. Hassenforder, C. R. Acad. Sci. Paris, Ser. I 336 (2003).