Variational formulation of the Fokker-Planck equation with decay : a particle approach

We introduce a stochastic particle system that corresponds to the Fokker–Planck equation with decay in the many-particle limit, and study its large deviations. We show that the large-deviation rate functional corresponds to an energy-dissipation functional in a Mosco-convergence sense. Moreover, we prove that the resulting functional, which involves entropic terms and the Wasserstein metric, is again a variational formulation for the Fokker–Planck equation with decay. Keywords: Large deviations; Fokker–Planck equation with decay; Wasserstein metric; gradient flow; Mosco convergence