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Monte Carlo simulation in the evaluation of the young functional values

A Young measure was introduced to provide extended solutions for some non-convex problems in variational calculus. Nowadays it is very important tool applied in various optimization problems. At the core of each engineering application of the Young measure is the computation of values of so-called Young functional i.e. certain application that assigns to any Carathéodory function an integral with respect to related Young measure. However, calculating such values on the basis of its formal definition is a very difficult task which can be solved only in the most simple cases. In the paper we present some Monte Carlo method that allows one to evaluate the Young functional values in a case where the Young measure is associated with a certain class of rapidly oscillating sequences.