Abstract
Let X1...Xn be a sequence of i.i.d. positive or negative integer valued random variables and Hn=max(X_i+...+X_j) for 1<=i<=j<=n the local score of the sequence. The exact distribution of Hn is obtained using a simple Markov chain. This result is applied to the scoring of DNA and protein sequences in molecular biology.
Key words and phrases P-value, sequence analysis, local score, Markov chain.