Marco Rehmeier

activity

20182026

most citedOn nonlinear Markov processes in the sense of McKean

1 citations · 1 across the 16 of their papers we have counts for

collaborators

17 papers

math.PR2026

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…

math.PR2026

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…

math.PR2025

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 $Δ_{p} f = d i v (∣\nabla f ∣^{p - 2} \nabla f)$ for $p > 1$ and $q > 0$ , which is a simultaneous…

math.AP2024

Non-uniqueness of Leray--Hopf solutions for the $3 D$ fractional Navier--Stokes equations perturbed by transport noise

Theresa Lange, Marco Rehmeier, Andre Schenke

For the $3 D$ fractional Navier--Stokes equations perturbed by transport noise, we prove the existence of infinitely many Hölder continuous analytically weak, probabilistically stro…

math.PR2024

$p$ -Brownian motion and the $p$ -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 $p$ -Laplace equation in the same way as Brownian mo…

math.AP2024

$2 D$ 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 $2 D$ Euler equations in vorticity form on the full plane. First, we establish a generalized Lagrangian representation of…

math.PR2024

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…

math.PR2024

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…

math.AP2023

Weighted $L^{1}$ -semigroup approach for nonlinear Fokker--Planck equations and generalized Ornstein--Uhlenbeck processes

Marco Rehmeier

For the nonlinear Fokker--Planck equation $\partial_{t} u = Δ β (u) - \nablaΦ \cdot \nabla β (u) - d i v_{ϱ} (D (x) b (u) u), (t, x) \in (0, \infty) \times R^{d},$ where…

math.AP2023

Nonlinear Fokker--Planck--Kolmogorov equations as gradient flows on the space of probability measures

Marco Rehmeier, Michael Röckner

We propose a general method to identify nonlinear Fokker--Planck--Kolmogorov equations (FPK equations) as gradient flows on the space of probability measures on $R^{d}$ with…

math.PR2022★ 1 cited

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 $P_{s, ζ}$ , $s \geq 0$ , on path space,…

math.DS2022

Emergence of phase-locked states for a deterministic and stochastic Winfree model with inertia

Myeongju Kang, Marco Rehmeier

We study the emergence of phase-locking for Winfree oscillators under the effect of inertia. It is known that in a large coupling regime, oscillators governed by the deterministic…

math.PR2022

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…

math.PR2021

Nonuniqueness in law for stochastic hypodissipative Navier-Stokes equations

Marco Rehmeier, Andre Schenke

We study the incompressible hypodissipative Navier-Stokes equations with dissipation exponent $0 < α < \frac{1}{2}$ on the three-dimensional torus perturbed by an additive Wiener no…

math.PR2020

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…

math.PR2019

Existence of flows for linear Fokker-Planck-Kolmogorov equations and its connection to well-posedness

Marco Rehmeier

Let the coefficients $a_{ij}$ and $b_{i}$ , $i, j \leq d$ , 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…

math.PR2018

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…

Brownian motion in Minkowski normed spaces

Non-uniqueness of nonlinear Markov processes in the sense of McKean associated with parabolic PDEs

The Leibenson process

Non-uniqueness of Leray--Hopf solutions for the 3D fractional Navier--Stokes equations perturbed by transport noise

p-Brownian motion and the p-Laplacian

2D vorticity Euler equations: Superposition solutions and nonlinear Markov processes

Average dissipation for stochastic transport equations with Lévy noise

Remarks on regularization by noise, convex integration and spontaneous stochasticity

Weighted L1-semigroup approach for nonlinear Fokker--Planck equations and generalized Ornstein--Uhlenbeck processes

Nonlinear Fokker--Planck--Kolmogorov equations as gradient flows on the space of probability measures

On nonlinear Markov processes in the sense of McKean

Emergence of phase-locked states for a deterministic and stochastic Winfree model with inertia

Flow selections for (nonlinear) Fokker-Planck-Kolmogorov equations

Nonuniqueness in law for stochastic hypodissipative Navier-Stokes equations

Linearization and a superposition principle for deterministic and stochastic nonlinear Fokker-Planck-Kolmogorov equations

Existence of flows for linear Fokker-Planck-Kolmogorov equations and its connection to well-posedness

On Cherny's results in infinite dimensions: A theorem dual to Yamada-Watanabe

Non-uniqueness of Leray--Hopf solutions for the $3 D$ fractional Navier--Stokes equations perturbed by transport noise

$p$ -Brownian motion and the $p$ -Laplacian

$2 D$ vorticity Euler equations: Superposition solutions and nonlinear Markov processes

Weighted $L^{1}$ -semigroup approach for nonlinear Fokker--Planck equations and generalized Ornstein--Uhlenbeck processes