Content:
Both stochasctic programs with recourse and stochastic programs with chance constraints involve integral functionals that, except in some very special cases, are very difficult to evaluate numerically. One usually has to be satisfied with some approximation scheme that replaces the underlying probability measure with a discrete one obtained either from the partitioning of the sample space or as the empirical measure derived from a sample of the random quantities. In this latter instance, one needs to justify that the solution derived with the empirical measure is, at least in a probabilistic sense, an approximate solution. This paper deals with such a justification without making the usual assumption that the sample points have been obtained from independent experiments.
The motivation come from situations when the sample is generated by a stationary process such as a times series. Samples obtained from aplications involving atmospheric or environmental observations over time usually don't satisfy the independence assumption.
The proof of the Ergodic Theorem relies on the `scalarization' of random lsc function which associates with a random lsc function a countable collection of extended resl-valued variables that completely identify this random lsc function.
January '99