LOCAL SCORE DISTRIBUTION FOR MARKOVIAN CASE

Let A =(Ai)1≤i≤n be a sequence of letters taken in a finite alphabet Θ. Let s:Θ → Z be a scoring function and X =(Xi)1≤i≤n the corresponding score sequence where Xi = s(Ai). The local score is defined as follows: Hn = ∑j max1≤i≤j≤n k=i Xk. 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. Key words and phrases: Markov chain, local score, P-value, sequence analysis. 1