TIME-DICRETIZATION FOR CONTROLLED MARKOV-PROCESSES .1. GENERAL APPROXIMATION RESULTS

The method of time-discretization is investigated in order to approxim ate finite horizon cost functions for continuous-time stochastic contr ol problems. The approximation method is based on approximating time-d ifferential equations by one-step difference methods. In this paper ge neral approximation results will be developed. An approximation lemma is presented. This lemma enables us to conclude orders of converge, wh ich makes the method of computational interest. Also unbounded cost fu nctions are allowed. We concentrate on approximations induced by discr ete-time controlled Markov processes. The approximation can in princip le be computed recursively by using discrete-time dynamic programming. In a subsequent second paper two applications will be studied in deta il.