8 papers · 1 filter
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…
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, Iulian Cîmpean +2
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…
Sharp Non-uniqueness in Law for Stochastic Differential Equations on the Whole Space
Huaxiang Lü, Michael Röckner
In this paper, we investigate the stochastic differential equation on : \begin{align*} \dif X_t&=v(t,X_t)\dif t+\sqrt{2} \dif W_t. \end{align*} For any finite…
The Leibenson process
Viorel Barbu, Sebastian Grube, Marco Rehmeier +1
Consider the Leibenson equation \begin{equation*} \partial_t u = Î_p u^q, \end{equation*} where for and , which is a simultaneo…
Nonlinear Fokker-Planck equations as smooth Hilbertian gradient flows
Viorel Barbu, Michael Röckner
Under suitable assumptions on and , the nonlinear Fokker-Planck equation $u_t…