TY - GEN A1 - Disser, Karoline A1 - Liero, Matthias T1 - On gradient structures for Markov chains and the passage to Wasserstein gradient flows N2 - We study the approximation of Wasserstein gradient structures by their finite-dimensional analog. We show that simple finite-volume discretizations of the linear Fokker-Planck equation exhibit the recently established entropic gradient-flow structure for reversible Markov chains. Then we reprove the convergence of the discrete scheme in the limit of vanishing mesh size using only the involved gradient-flow structures. In particular, we make no use of the linearity of the equations nor of the fact that the Fokker-Planck equation is of second order. KW - Wasserstein gradient flow KW - relative entropy KW - finite-volume scheme KW - entropy/entropy-dissipation formulation KW - Markov chains KW - gradient structures Y1 - 2014 UR - https://opus4.kobv.de/opus4-matheon/frontdoor/index/index/docId/1273 UR - https://nbn-resolving.org/urn:nbn:de:0296-matheon-12730 ER -