![]() ![]() The technical core of this machinery is the introduction of a pair of intertwined space-time paraproducts on parabolic Holder spaces, with good continuity properties, as well as some continuity properties of iterated commutators and correctors built from paraproducts and resonant operators. We develop for that purpose a higher order paracontrolled calculus via semigroups methods. ![]() We sharpen in this work the tools of paracontrolled calculus in order to provide a complete analysis of the parabolic Anderson model equation in a 3-dimensional setting, in either bounded or unbounded domains equipped with a sub-Laplacian structure.
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