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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 = Δ_p u^q, \end{equation*} where for and , which is a simultaneous…
-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…
Average dissipation for stochastic transport equations with Lévy noise
Franco Flandoli, Andrea Papini, Marco Rehmeier
We show that, in one spatial and arbitrary jump dimension, the averaged solution of a Marcustype SPDE with pure jump Lévy transport noise satisfies a dissipative deterministic equa…
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…
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,…
Flow selections for (nonlinear) Fokker-Planck-Kolmogorov equations
Marco Rehmeier
We provide a method to select flows of solutions to the Cauchy problem for linear and nonlinear Fokker--Planck--Kolmogorov equations (FPK equations) for measures on Euclidean space…
Nonuniqueness in law for stochastic hypodissipative Navier-Stokes equations
Marco Rehmeier, Andre Schenke
We study the incompressible hypodissipative Navier-Stokes equations with dissipation exponent on the three-dimensional torus perturbed by an additive Wiener no…
Linearization and a superposition principle for deterministic and stochastic nonlinear Fokker-Planck-Kolmogorov equations
Marco Rehmeier
We prove a superposition principle for nonlinear Fokker-Planck-Kolmogorov equations on Euclidean spaces and their corresponding linearized first-order continuity equation over the…
Existence of flows for linear Fokker-Planck-Kolmogorov equations and its connection to well-posedness
Marco Rehmeier
Let the coefficients and , , of the linear Fokker-Planck-Kolmogorov equation (FPK-eq.) $$\partial_tμ_t = \partial_i\partial_j(a_{ij}μ_t)-\partial_i(b_iμ_t…
On Cherny's results in infinite dimensions: A theorem dual to Yamada-Watanabe
Marco Rehmeier
We prove that joint uniqueness in law and the existence of a strong solution imply pathwise uniqueness for variational solutions to stochastic partial differential equations of the…