Semi-Markov control processes with unknown holding times distribution under a discounted criterion

The paper deals with a class of semi-Markov control models with Borel state and control spaces, possibly unbounded costs, and unknown holding times distribution H. Assuming that H does not depend on state-action pairs, we combine suitable methods of statistical estimation of H with control procedures to construct an asymptotically discounted optimal policy [InlineMediaObject not available: see fulltext.] and an optimal stationary policy { f ∞ }, where f n converges to f ∞ in the sense of Schäl [12]. Copyright Springer-Verlag 2005