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Remarks about discrete Young measures and their Monte Carlo simulation

Grzybowski A., Puchała P.

Journal of Applied Mathematics and Computational Mechanics

2015

Vol. 14, nr 2

13--20

This article is devoted to the problem of simulation of random variables distributed according to Young measures associated with piecewise affine functions determined on bounded intervals. We start with simple functions which can take on a finite number of different values with inverse images being the intervals or their unions. We present some formal results connected with related discrete Young measures and propose an algorithm for generating random variables having such distributions. Next, based on these results we introduce an algorithm designed for approximation of Young measures in various, more general situations. We also present an example where a Young measure associated with a piecewise affine function is approximated with the help of computer simulations. In this benchmarking problem the theoretical results are compared with the ones obtained in the Monte Carlo experiment.

The Phenomena of the Infi-calculus in Elementary Mathematics

Eisenmann P.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

2000/2001

Vol. 8

125--130