187 citations · 462 across the 62 of their papers we have counts for
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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 = Δ_p u^q, \end{equation*} where for and , which is a simultaneous…
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 .…
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-…
-Brownian motion and the -Laplacian
Viorel Barbu, Marco Rehmeier, Michael Röckner
In this paper we construct a stochastic process, more precisely, a (nonlinear) Markov process, which is related to the parabolic -Laplace equation in the same way as Brownian mo…
Distribution-flow dependent SDEs driven by (fractional) Brownian motion and Navier-Stokes equations
Zimo Hao, Michael Röckner, Xicheng Zhang
Motivated by the probabilistic representation for solutions of the Navier-Stokes equations, we introduce a novel class of stochastic differential equations that depend on the entir…