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Renormalising SPDEs in regularity structures

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arxiv 1711.10239 v4 pith:ZT2L7JAG submitted 2017-11-28 math.AP math.PR

Yvain Bruned , Ajay Chandra , Ilya Chevyrev , Martin Hairer This is my paper
classification math.APmath.PR
keywords regularityrenormalisationactionarxivbphzclasscorrespondingdriving
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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.

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Cited by 3 Pith papers

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