84 citations · 987 across the 100 of their papers we have counts for
114 papers
Existence and Ergodicity for Nonlinear Fokker-Planck Equations for Probability Density Functions
Xing Huang, Michael Röckner, Feng-Yu Wang
For a class of nonlinear Fokker-Planck equations for probability densities, we construct distributional solutions by using an approximation scheme with nonlinear Neumann problems i…
Uniqueness for nonlinear Fokker-Planck equations with general diffusion terms and their associated nonlinear Markov processes
Viorel Barbu, Yuqi Li, Michael Röckner
This work is concerned with the uniqueness of distributional solutions to nonlinear Fokker-Planck equations with non-diagonal diffusion terms of type \begin{equation} u_{t}-\sum_{i…
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…
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 wit…
The stochastic evolution of an infinite population with logistic-type interaction
Yuri Kozitsky, Michael Röckner
An infinite population of point entities dwelling in the habitat $X=\mathds{R}^d$ is studied. Its members arrive in and depart from at random. The departure rate has a term cor…
SVI solutions to stochastic nonlinear diffusion equations on general measure spaces
Benjamin Gess, Michael Röckner, Weina Wu
We establish a framework for the existence and uniqueness of solutions to stochastic nonlinear (possibly multi-valued) diffusion equations driven by multiplicative noise, with the…