LOW DISCOUNTING AND THE UPPER LONG-RUN AVERAGE VALUE IN DYNAMIC-PROGRAMMING

Consider a dynamic programming problem, where the discounted value fun ctions converge to a limit function as the discount factor tends to 1. It is proved that the limit function must be the Markov upper long-ru n average value function, if the convergence holds in the weak topolog y on the space of all bounded measurable functions on the state space. Necessary and sufficient conditions for the existence of the weak lim it are given. The results are applied to compact continuous dynamic pr ogramming problems used extensively in economics. (C) 1994 Academic Pr ess, Inc.