A Priori Bounds for the Generalized Parabolic Anderson Model

Explore a 37-minute conference talk on the generalised parabolic Anderson model (gPAM) delivered at the Workshop on "Stochastic Partial Differential Equations" held at the Erwin Schrödinger International Institute for Mathematics and Physics. Delve into the challenges of controlling gPAM over large scales in path-wise frameworks, a long-standing open problem in the field. Discover how the roughness of noise at small scales complicates large-scale behavior analysis of gPAM and learn about recent advancements in overcoming these difficulties. Gain insights into the robust local well-posedness theory for gPAM, which allows for a wider class of rough driving noises, as developed through path-wise approaches like regularity structures and paracontrolled calculus. Understand the significance of this research in the context of multiplicative singular SPDEs and its implications for studying stochastic partial differential equations.