Удк 519.2 Distribution of Functionals of Solutuions in Some Stochastic Variational Problems

The problem under consideration is as follows. Let I(u, ω) be a random functional of u , u is an element of some functional space R, ω being a random parameter. For each ω, one seeks for a minimum value of the functional I(u, ω). The minimizing element, ǔ, of the functional I(u, ω) is random since it depends on ω. We are interested in determining the probability density function of some deterministic functional, L(ǔ), of the minimizing element. In such general setting one can hardly expect a meaningful answer. In this note a very special case of the problem is considered when I(u, ω) is a quadratic functional,