We prove a general equivalence statement between the notions of models and modelled distribution over a regularity structure, and paracontrolled systems indexed by the regularity structure. This takes in particular the form of a parametrisation of the set of models over a regularity structure by the set of reference functions used in the paracontrolled representation of these objects. The construction of a modelled distribution from a paracontrolled system is explicit, and takes a particularly simple form in the case of the BHZ regularity structures used for the study of singular stochastic partial differential equations.
|Publication status||Published - Dec 18 2019|
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