Author
Bruned, Y
Chandra, A
Chevyrev, I
Hairer, M
Journal title
Journal of the European Mathematical Society
Last updated
2020-09-27T04:18:48.79+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
Download URL
http://arxiv.org/abs/1711.10239
Publication type
Journal Article
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