Convergence rate to equilibrium in Wasserstein distance for reflected jump–diffusions

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...

On the rate of convergence in Wasserstein distance of the empirical measure

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 ‖ ...

Convergence in the Wasserstein Metric for MarkovChain

This paper gives precise bounds on the convergence time of the Gibbs sampler used in the Bayesian restoration of a degraded image. Convergence to stationarity is assessed using the Wasserstein metric, rather than the usual choice of total variation distance. The Wasserstein metric may be more easily applied in some applications, particularly those on continuous state spaces. Bounds on convergen...

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...