ABSTRACT
As a first application of the preceding estimates, we consider a typical ergodic control of diffusions with jumps, based on the papers by Garroni and Menaldi [40] and Menaldi and Robin [79]. Here, we discuss ergodicity properties of optimal stopping time problems for jumps diffusion processes reflected from the boundary of a bounded domain. This is perhaps the simplest control model in which the controller can decide whether or not to stop the evolution of the dynamic system. The dynamic programming technique yields a set of complementary inequalities to be satisfied by the optimal solution, which is well interpreted as a variational inequality or complementary problem, in our case an ergodic variational inequality.
