On the Epiconvergence of Stochastic Optimization Problems

The problem of strong consistency of sequences of optimal solutions to stochastic optimization problems is considered. This problem is related to a large number of applications including Bayesian decision problems and Monte Carlo simulations, as well as a number of statistical methodologies such as maximum likelihood estimation. The theory of epiconvergence being a framework within which such results can be established, the epiconvergence of the performance criteria of a sequence of stochastic optimization problems is proved under simple weak assumptions.