… of dynamical systems introducing a fiber characteristic equation, at least in the context …
measure theory, ie, by treating the digraph limits as a measure-valued function (digraph measures …

… as a diagraph measure (DGM) and derive the resulting Vlasov-Fokker-Plank equation in the
stochastic … However, in both cases, we will obtain the same Vlasov-Fokker-Plank equation. …

… Using a particular Laplace principle associated with the vector of empirical measures (see …
measure π N as its stationary distribution. To this end, let us first introduce the directed graph ( …

… well as approximation of solutions to the generalized Vlasov equation, let us first investigate
properties of Fβ. To construct approximations of the digraph measures as well as the initial …

… –Vlasov equations as a meanfield formulation of a system of interacting stochastic McKean
(or noisy Kuramoto-type) differential equations with … Vlasov equations on digraph measures. …

… measures, motivated by the recent work in [Kuehn, Xu. Vlasov equations on digraph
measures… Under a mild condition on the initial graph measure, we show that the graph measures …

… consists of keeping the trajectories of (8), taking the mean field limit by embedding trajectories
with an empirical measure on Ω×IRd to solutions of the Vlasov equation (or continuity …

… Vlasov equation (1.4)-(1.5) by a fixed-point argument relying on the Lipschitz regularity of the
force F in (1.5) with respect to the measure µt, … discretizations of digraph measures by finite …

… such as digraph measures [35] or … digraph measure), then the microscopic system can be
shown to converge weakly towards a measure µ ∈ C([0, T], P([0, 1] × Rd)), solution to a Vlasov …

… non-interchangeable graph structures defined by wij into a simple limiting Vlasov equation …
digraph measures B([0, 1], M([0, 1]) consists of everywhere defined in ξ bounded measures in …