  In this paper we provide an alternative approach to the works of the
physicists S. Cocco and R. Monasson about a model of DNA molecules. The aim is
to predict the sequence of bases by mechanical stimulations. The model
described by the physicists is a stopped birth and death process with unknown
transition probabilities. We consider two models, a discrete in time and a
continuous in time, as general as possible. We show that explicit formula can
be obtained for the probability to be wrong for a given estimator, and apply it
to evaluate the quality of the prediction. Also we add some generalizations
comparing to the initial model allowing us to answer some questions asked by
the physicists.
