Publication at Faculty of Mathematics and Physics |
2007
Abstract
Stochastic optimization programs can be considered as functions of probability measures defined either on a finite or an infinite space. Thus, it is natural to ask on sensitivity of such an optimization program to a perturbation of that probability measure.
Particularly, we address estimation based on observed data. The main obstacle arises from random features of the considered program approximation.
We are meeting the question on measurability of studied objects and on existence of a convenient measurable selection. In this paper we present a pointwise approach which allows us overcome a lack of measurability.