Value iteration and rolling plans for Markov control processes with unbounded rewards

The authors study the convergence of value-iteration functions and the existence of error bounds for rolling horizon procedures in discrete-time Markov control processes with Borel state and control spaces, and unbounded reward functions with a discount factor. As expected, in contrast to the bounded case, the bounds are `pointwise,´ not `uniform´. In addition, it is shown how the error bound in the weighted norm case can be improved by introducing appropriate ergodicity conditions