Malliavin calculus for regularity structures: The case of gPAM

G Cannizzaro (1) , P K Friz (1, 2) , Paul Gassiat (3)

1 TU - Technical University of Berlin / Technische Universität Berlin
2 WIAS - Weierstraß-Institut für Angewandte Analysis und Stochastik = Weierstrass Institute for Applied Analysis and Stochastics [Berlin]
3 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

Malliavin calculus is implemented in the context of [M. Hairer, A theory of regularity structures, Invent. Math. 2014]. This involves some constructions of independent interest, notably an extension of the structure which accomodates a robust, and purely deterministic, translation operator, in L 2-directions, between " models ". In the concrete context of the generalized parabolic Anderson model in 2D-one of the singular SPDEs discussed in the afore-mentioned article-we establish existence of a density at positive times.

Domaines: Probabilités [math.PR]

G Cannizzaro, P K Friz, Paul Gassiat. Malliavin calculus for regularity structures: The case of gPAM. Journal of Functional Analysis, 2017, 272, pp.363 - 419. ⟨10.1016/j.jfa.2016.09.024⟩. ⟨hal-01419769⟩