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math.PR2024
-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…
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…