Exact distribution of the local score for markovian sequences

Let A = (A(i))(1 <= i <= n) be a sequence of letters taken in a finite alphabet Theta. Let s : Theta --> Z be a scoring function and X = (X-i)(1 <= i <= n) the corresponding score sequence where X-i = s(A(i)). The local score is defined as follows: H-n = max(1 <= i <= j <= n) Sigma(j)(k= i) X-k. We provide the exact distribution of the local score in random sequences in several models. We will first consider a Markov model on the score sequence X, and then on the letter sequence A. The exact P-value of the local score obtained with both models are compared thanks to several datasets. They are also compared with previous results using the independent model.