Generalized Orlicz spaces and Wasserstein distances for convex-concave scale functions

Details Generalized Orlicz spaces and Wasserstein distances for convex-concave scale functions Generalized Orlicz spaces and Wasserstein distances for convex-concave scale functions

2011-04-21

arxiv.org/abs/1104.4223v1

Mathematics

Functional Analysis

Scientific paper

Given a strictly increasing, continuous function $\vartheta:\R_+\to\R_+$, based on the cost functional $\int_{X\times X}\vartheta(d(x,y))\,d q(x,y)$, we define the $L^\vartheta$-Wasserstein distance $W_\vartheta(\mu,\nu)$ between probability measures $\mu,\nu$ on some metric space $(X,d)$. The function $\vartheta$ will be assumed to admit a representation $\vartheta=\phi\circ\psi$ as a composition of a convex and a concave function $\phi$ and $\psi$, resp. Besides convex functions and concave functions this includes all $\mathcal C^2$ functions. For such functions $\vartheta$ we extend the concept of Orlicz spaces, defining the metric space $L^\vartheta(X,m)$ of measurable functions $f: X\to\R$ such that, for instance, $$d_\vartheta(f,g)\le1\quad\Longleftrightarrow\quad \int_X\vartheta(|f(x)-g(x)|)\,d\mu(x)\le1.$$

Affiliated with

Also associated with

No associations

Rating

Generalized Orlicz spaces and Wasserstein distances for convex-concave scale functions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Generalized Orlicz spaces and Wasserstein distances for convex-concave scale functions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Generalized Orlicz spaces and Wasserstein distances for convex-concave scale functions will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-178102