Induced geometry

We study several constrained variational problems in the 2-Wasserstein metric for which the set of probability densities satisfying the constraint is not closed. For example, given a probability density F0 on Rd and a time-step 2 h 0, we seek to minimize I(F ) = hS(F )+W2 (F0 , F ) over all of the probability densities F that have the same mean and variance as F0 , where S(F ) is the entropy of F . We prove existence of minimizers. We also analyze the induced geometry of the set of densities satisfying the constraint on...

41p tuanloccuoi 04-01-2013 49 7   Download

Geometry is a branch of mathematics related research space. Using experience, or perhaps by intuition, it is recognized by the space fundamental characteristics, the geometric axioms called the system. Axiomatic system including the original concept is not defined and the axioms (also known as the proposition) does not prove a relationship defined between the concepts.

12p phalinh14 07-08-2011 47 3   Download