Renormalising SPDEs in regularity structures

Author: 

Bruned, Y
Chandra, A
Chevyrev, I
Hairer, M

Journal: 

Journal of the European Mathematical Society

Last Updated: 

2019-09-21T00:34:10.817+01:00

abstract: 

The formalism recently introduced in arXiv:1610.08468 allows one to assign a regularity structure, as well as a corresponding "renormalisation group", to any subcritical system of semilinear stochastic PDEs. Under very mild additional assumptions, it was then shown in arXiv:1612.08138 that large classes of driving noises exhibiting the relevant small-scale behaviour can be lifted to such a regularity structure in a robust way, following a renormalisation procedure reminiscent of the BPHZ procedure arising in perturbative QFT.

The present work completes this programme by constructing an action of the renormalisation group onto a suitable class of stochastic PDEs which is intertwined with its action on the corresponding space of models. This shows in particular that solutions constructed from the BPHZ lift of a smooth driving noise coincide with the classical solutions of a modified PDE. This yields a very general black box type local existence and stability theorem for a wide class of singular nonlinear SPDEs.

Symplectic id: 

991805

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Submitted to ORA: 

Submitted

Publication Type: 

Journal Article