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Malliavin calculus for regularity structures: The case of gPAM

Cannizzaro, G.; Friz, Peter K.; Gassiat, Paul (2017), Malliavin calculus for regularity structures: The case of gPAM, Journal of Functional Analysis, 272, 1, p. 363-419. 10.1016/j.jfa.2016.09.024

Type
Article accepté pour publication ou publié
External document link
https://arxiv.org/abs/1511.08888v1
Date
2017
Journal name
Journal of Functional Analysis
Volume
272
Number
1
Publisher
Elsevier
Pages
363-419
Publication identifier
Metadata
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Author(s)
Cannizzaro, G.

Friz, Peter K.

Gassiat, Paul
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)
Malliavin calculus is implemented in the context of Hairer (2014) [16]. This involves some constructions of independent interest, notably an extension of the structure which accommodates a robust, and purely deterministic, translation operator, in L2L2-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.
Subjects / Keywords
Regularity structures; Malliavin calculus; Generalized parabolic Anderson model; Singular SPDEs