0
votes
0answers
49 views

Maximizing the “uniformity” of a probability measure, with constraints, via path length minimization

Background I want to find a probability measure for a continuous random variable, subject to moment constraints, that is maximally "uniform", as defined below: Definition: Maximally Uniform ...
2
votes
1answer
247 views

Upper bound on the maxima of ratio of expectation of quantities under Gaussian measure

Let $\lambda,\eta >0$ be given, and $u:\mathbb{R}\rightarrow \mathbb{R}$ be a real valued function. Define $$\Delta(u)= \frac{\int u(h) \exp(-\eta ...
9
votes
0answers
354 views

Maximizing the volume in a family of subsets of a cube

Starting from a question in probability, one is eventually lead to the following optimization problem. Let $I:=[0,\\, 1],$ and let $A$ be a Lebesgue measurable subset of the $n$-dimensional cube, ...