Existence of densities for the dynamic \(\Phi^4_3\) model. (English. French summary) Zbl 1456.60137

Gassiat, Paul; Labbé, Cyril

Ann. Inst. Henri Poincaré, Probab. Stat. 56, No. 1, 326-373 (2020).

Summary: We apply Malliavin calculus to the \(\Phi^4_3\) equation on the torus and prove existence of densities for the solution of the equation evaluated at regular enough test functions. We work in the framework of regularity structures and rely on Besov-type spaces of modelled distributions in order to prove Malliavin differentiability of the solution. Our result applies to a large family of Gaussian space-time noises including white noise, in particular the noise may be degenerate as long as it is sufficiently rough on small scales.

MSC:

60H07	Stochastic calculus of variations and the Malliavin calculus
60H15	Stochastic partial differential equations (aspects of stochastic analysis)

Keywords:

Malliavin calculus; regularity structures; stochastic quantization equation; singular SPDE

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