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.
DFG Programme
CRC/Transregios
