  We consider dynamic programming problems with a large time horizon, and give
sufficient conditions for the existence of the uniform value. As a consequence,
we obtain an existence result when the state space is precompact, payoffs are
uniformly continuous and the transition correspondence is non expansive. In the
same spirit, we give an existence result for the limit value. We also apply our
results to Markov decision processes and obtain a few generalizations of
existing results.
