Generalized Wasserstein Distance and Weak Convergence of Sublinear Expectations

Weak and strong convergence theorems for a finite family of generalized asymptotically quasinonexpansive nonself-mappings

In this paper, we introduce and study a new iterative scheme toapproximate a common xed point for a nite family of generalized asymptoticallyquasi-nonexpansive nonself-mappings in Banach spaces. Several strong and weakconvergence theorems of the proposed iteration are established. The main resultsobtained in this paper generalize and rene some known results in the currentliterature.

Convergence to equilibrium in Wasserstein distance for Fokker-Planck equations

We describe conditions on non-gradient drift diffusion Fokker-Planck equations for its solutions to converge to equilibrium with a uniform exponential rate in Wasserstein distance. This asymptotic behaviour is related to a functional inequality, which links the distance with its dissipation and ensures a spectral gap in Wasserstein distance. We give practical criteria for this inequality and co...

Non-monotone Convergence in the Quadratic Wasserstein Distance

We give an easy counter-example to Problem 7.20 from C. Villani’s book on mass transport: in general, the quadratic Wasserstein distance between n-fold normalized convolutions of two given measures fails to decrease monotonically. We use the terminology and notation from [5]. For Borel measures μ, ν on R we define the quadratic Wasserstein distance T (μ, ν) := inf (X,Y ) E [ ‖X − Y ‖ ] where ‖ ...

Weak Convergence of Generalized U - Statistics

Wasserstein Distance Measure Machines

This paper presents a distance-based discriminative framework for learning with probability distributions. Instead of using kernel mean embeddings or generalized radial basis kernels, we introduce embeddings based on dissimilarity of distributions to some reference distributions denoted as templates. Our framework extends the theory of similarity of Balcan et al. (2008) to the population distri...