8 papers
Brownian motion in Minkowski normed spaces
Shin-ichi Ohta, Marco Rehmeier, Kohei Suzuki
A Minkowski normed space is the Euclidean space equipped with a (possibly asymmetric) uniformly convex and smooth norm, forming a particular class of Finsler manifolds. We construc…
Non-uniqueness of nonlinear Markov processes in the sense of McKean associated with parabolic PDEs
Ehsan Abedi, Florian Bechtold, Marco Rehmeier
We derive a general scheme to construct infinitely many probabilistic counterparts for solutions to nonlinear PDEs by recasting the latter as different nonlinear Fokker--Planck equ…
vorticity Euler equations: Superposition solutions and nonlinear Markov processes
Marco Rehmeier, Marco Romito
In this note we contribute two results to the theory of the Euler equations in vorticity form on the full plane. First, we establish a generalized Lagrangian representation of…
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…
-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…
Non-uniqueness of Leray--Hopf solutions for the fractional Navier--Stokes equations perturbed by transport noise
Theresa Lange, Marco Rehmeier, Andre Schenke
For the fractional Navier--Stokes equations perturbed by transport noise, we prove the existence of infinitely many Hölder continuous analytically weak, probabilistically str…