chiro, I do not understand your suggestion, why should I consider products of functions that are concave? I cannot see how such products arise from the problem that I stated.
Just to make things clear: in my problem, H is a function of the probability distribution p(x) (e.g. the variance) and...
Given two (dependent) random variables X and Y with joint PDF p(x,y) =p(x|y)p(y) =p(y|x)p(x), let H[X] be real-valued concave function of p(x), and H[X|Y] the expectation of H of p(x|y) with respect to p(y).
Examples of possible functions H include the entropy of X, or its variance.
The...