Project A01
Energy solutions, singular SPDEs on large scales and stochastic homogenization

Project description

While we now have a good understanding of pathwise local properties of scaling subcritical singular SPDEs, probabilistic aspects and long-term/large-scale behavior remain less clear. Energy solutions offer a probabilistic view for some singular SPDEs, based on martingale arguments and Fock space analysis. Our project will further develop the theory of energy solutions and focus on homogenisation of non-symmetric SDEs. A key objective is to explore dissipative effects of Burgers nonlinearities in Fock space and to analyze the well-posedness and non-Gaussianity of critical and supercritical singular SPDEs.

Principal Investigators

Felix Otto (MPI Leipzig)

Nicolas Perkowski (FU Berlin)

Project members

Immanuel Zachhuber (FU Berlin)

Publications

Preprints

• Gräfner, L., Perkowski, N., Popat, S., 2024. Energy solutions of singular SPDEs on Hilbert spaces with applications to domains with boundary conditions. https://doi.org/10.48550/ARXIV.2411.07680

• Gräfner, L., Perkowski, N., 2024. Weak well-posedness of energy solutions to singular SDEs with supercritical distributional drift. https://doi.org/10.48550/ARXIV.2407.09046