Wasserstein stability estimates for covariance-preconditioned Fokker-Planck equations

2019/10/16 by Carrillo, J. A., Vaes, U. · 2 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1910.07555

Abstract

We study the convergence to equilibrium of the mean field PDE associated with the derivative-free methodologies for solving inverse problems. We show stability estimates in the euclidean Wasserstein distance for the mean field PDE by using optimal transport arguments. As a consequence, this recovers the known convergence towards equilibrium estimates in the case of a linear forward model.

Cited by

• Solving Inverse Problems via Diffusion-Based Priors: An Approximation-Free Ensemble Sampling Approach
• New affine invariant ensemble samplers and their dimensional scaling

Related

• Optimal non-symmetric Fokker-Planck equation for the convergence to a given equilibrium
• Sharp Decay of the Fisher Information for Degenerate Fokker-Planck Equations
• Hypocoercivity in Wasserstein-1 for the kinetic Fokker-Planck equation via Malliavin Calculus
• Existence and Stability for Fokker-Planck equations with log-concave reference measure
• Variational structures for the Fokker--Planck equation with general Dirichlet boundary conditions