A general paracontrolled ansatz built from decorated trees and iterated paraproducts gives local well-posedness and BPHZ renormalisation for a broad class of subcritical parabolic singular SPDEs.
A note on the Taylor estimates of iterated paraproducts
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abstract
Bony's paraproduct is one of the main tools in the theory of paracontrolled calculus. The paraproduct is usually defined via Fourier analysis, so it is not a local operator. In the previous researches [7, 8], however, the author proved that the pointwise estimate like (1.2) holds for the paraproduct and its iterated versions when the sum of the regularities is smaller than 1. The aim of this article is to extend these results for higher regularities.
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A general paracontrolled ansatz for singular SPDEs
A general paracontrolled ansatz built from decorated trees and iterated paraproducts gives local well-posedness and BPHZ renormalisation for a broad class of subcritical parabolic singular SPDEs.