14 papers
Homogenization of diffusions on the lattice with periodic drift coefficients; Application of logarithmic Sobolev inequality
Sergio Albeverio, Michael Rockner, Simonetta Bernabei +1
A homogenization problem of infinite dimensional diffusion processes indexed by having periodic drift coefficients is considered. By an application of the uniform e…
Infinite-dimensional nonlinear stationary Fokker-Planck-Kolmogorov equations
Vladimir I. Bogachev, Michael Röckner, Stanislav V. Shaposhnikov
We prove existence of a probability solution to the nonlinear stationary Fokker-Planck-Kolmogorov equation on an infinite dimensional space with a centered Gaussian measure wi…
Nonlocal, nonlinear Fokker-Planck equations and nonlinear martingale problems
Viorel Barbu, José LuÃs da Silva, Michael Röckner
This work is concerned with the existence of mild solutions and the uniqueness of distributional solutions to nonlinear Fokker-Planck equations with nonlocal operators , w…
Probabilistic representation of solutions to the parabolic -Laplace equation
Viorel Barbu, Michael Röckner
This work is concerned with the probabilistic representation of solutions to the -Laplace evolution equation …
Stochastic intrinsic gradient flows on the Wasserstein space
Panpan Ren, Michael Röckner, Feng-Yu Wang +1
We construct stochastic gradient flows on the -Wasserstein space over for energy functionals of the type $W_F(Ïd x)=\int_{\mathbb R^d}F(x,Ï(x))d x…
Regularization of the superposition principle: Potential theory meets Fokker-Planck equations
Lucian Beznea, Iulian Cîmpean, Michael Röckner
For a solution to a (possibly nonlinear) Fokker-Planck equation (FPE) the powerful superposition principle renders a probability measure on path space with one dimensional time mar…