A Class of Multidimensional Oscillating Sequences and Related Young Functionals

In this paper, a class of sequences consisting of fast oscillating functions that are defined on multidimensional Euclidean space is defined. Next, some propositions providing probabilistic characterizations of Young measures connected with these sequences are stated. These propositions enable one to compute values of so-called Young functionals i.e. certain applications that assigns to any Carathodory function an integral with respect to related Young measure. These values are of primary interest in various contemporary non-convex optimization problems. Moreover, our results allow one to approximate the Young-functional's values by Monte Carlo simulations in all such cases where the integral cannot be computed explicitly. In this paper, a number of examples that illustrate possible applications of introduced formal results are provided as well.