An analytic BPHZ theorem for regularity structures

Understand

We prove a general theorem on the stochastic convergence of appropriately renormalized models arising from nonlinear stochastic PDEs.

• The theory of regularity structures gives a fairly automated framework for studying these problems but previous works had to expend significant effort to obtain these stochastic estimates in an ad-hoc manner.
• In contrast, the main result of this article operates as a black box which automatically produces these estimates for nearly all of the equations that fit within the scope of the theory of regularity structures.
• Our approach leverages multi-scale analysis strongly reminiscent to that used in constructive field theory, but with several significant twists.