Let us consider X = X1,...,Xn a sequence of Bernoulli or Markov observations and En an event depending on the sequence X. We suppose that it is possible to build from X an order one Markov chain Z = Z1,...,Zn on the finite state space  of size L. This space contains (in the order): k starting states denoted s1,...,sk, some intermediate states, and one final absorbing state f. The Markov chain is designed such as