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

Abstract

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 and an optimal stationary policy { f_∞}, where f _n converges to f_∞ in the sense of Schäl [12].