Analyzing the invariant (stationary) solutions of the Gauss-Galerkin Quadrature-Method-of-Moments closure of polynomial McKean-Vlasov SDEs, independently of the number of retained moments (not relying on truncation convergence). Key results: in the small-noise limit the closed system has as many stationary solutions as the potential has extrema - all critical points, not just minima - so the closure preserves the full equation's bifurcation diagram; a scaling property lets stability changes be probed directly. Applied to the Dawson-Shiino model. Belongs to nonlinear Fokker-Planck / mean-field diffusion theory.
This probability-theory paper analyzes the stationary (invariant) solutions of the Gauss-Galerkin Quadrature-Method-of-Moments (GG-QMoM) closure of McKean-Vlasov (mean-field) stochastic differential …