We construct weak solutions to the McKean–Vlasov SDE d X (t)= b (X (t), d LX (t) dx (X (t)))
dt+ σ (X (t), d LX (t) dt (X (t))) d W (t) on ℝ d for possibly degenerate diffusion matrices σ with …

One obtains a probabilistic representation for the entropic generalized solutions to a
nonlinear Fokker--Planck equation in R^d with a multivalued nonlinear diffusion term as …

We study nonlinear Markov processes in the sense of McKean's seminal work [29] and
present a large new class of examples. Our notion of nonlinear Markov property is in …

The paper is concerned with a McKean-Vlasov type SDE with drift in anisotropic Besov
spaces with negative regularity and with degenerate diffusion matrix under the weak H {\" o} …

Interacting diffusions approximating the porous medium equation and propagation of chaos
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We consider a porous media type equation over all of ℝ d, d= 1, with monotone
discontinuous coefficient with linear growth, and prove a probabilistic representation of its …

We consider a possibly degenerate porous media type equation over all of\mathbb R^ d with
d= 1, with monotone discontinuous coefficients with linear growth and prove a probabilistic …

We introduce a new class of nonlinear Stochastic Differential Equations in the sense of
McKean, related to non conservative nonlinear Partial Differential equations (PDEs). We …

The object of this paper is the uniqueness for a d-dimensional Fokker-Planck type equation
with inhomogeneous (possibly degenerated) measurable not necessarily bounded …

We study a large class of McKean–Vlasov SDEs with drift and diffusion coefficient
depending on the density of the solution's time marginal laws in a Nemytskii-type of way. A …