A Remark On Empirical Estimates In Multistage Stochastic Programming

A multistage stochastic programming problem can be introduced either as the problem considered with respect to some abstract mathematical space or as a system of parametric optimization problems considered with respect to the Euclidean space with an inner (recurrent) dependence and mathematical (mostly conditional) expectation in the objective functions of the individual problems. Consequently, this type of the problems belongs to the class of optimization problems depending on a probability measure. The aim of the paper is to treat the case when the theoretical underlying probability measure is replaced by an "empirical" one.