In this paper we consider the long run average continuous control problem of piecewise-deterministic Markov processes (PDP's for short). The control variable acts on the jump rate and transition measure Q of the PDP. The main goal of the paper is to characterize the optimality equation of the problem in terms of integro-differential equations for the continuous-time problem as well as in terms of embedded discrete-time Markov chains associated to the PDP.
Oswaldo Luiz V. Costa, François Dufour