Wasserstein stability estimates for covariance-preconditioned Fokker–Planck equations. (17th February 2021)

• Record Type: Journal Article
• Authors: Carrillo, J A; Vaes, U
• Is Part Of: Nonlinearity. Volume 34:Number 4(2021)
• Page Start: 2275
• Page End: 2295
• Publication Date: 2021-02-17
• Subjects: mean-field Fokker–Planck equation -- ensemble Kalman inversion -- Wasserstein stability estimates; 35Q70 -- 35Q84 -- 62F15 -- 65C35; Nonlinear theories -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis; Nonlinear theories; Periodicals; 515
• DOI: 10.1088/1361-6544/abbe62
• Languages: English
• ISSNs: 0951-7715

Abstract

Abstract: We study the convergence to equilibrium of the mean field PDE associated with the derivative-free methodologies for solving inverse problems that are presented by Garbuno-Inigo et al (2020 SIAM J. Appl. Dyn. Syst. 19 412–41), Herty and Visconti (2018 arXiv:1811.09387 ). 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 convergence towards equilibrium estimates by Garbuno-Inigo et al (2020 SIAM J. Appl. Dyn. Syst. 19 412–41) in the case of a linear forward model.