6 papers · 1 filter
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…
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…
On nonlinear Markov processes in the sense of McKean
Marco Rehmeier, Michael Röckner
We study nonlinear time-inhomogeneous Markov processes in the sense of McKean's seminal work [32]. These are given as families of laws , , on path space…
Remarks on regularization by noise, convex integration and spontaneous stochasticity
Franco Flandoli, Marco Rehmeier
This note is devoted to a discussion of the potential links and differences between three topics: regularization by noise, convex integration, spontaneous stochasticity. All of the…