Malliavin Calculus for regularity structures: the case of gPAM

2015/11/28 by Cannizzaro, Giuseppe, Friz, Peter K., Gassiat, Paul
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1511.08888

Abstract

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 L²-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.

Related

• Lecture notes on Malliavin calculus in regularity structures
• Lecture notes on tree-free regularity structures
• Malliavin Calculus and Density for Singular Stochastic Partial Differential Equations
• A Littlewood-Paley description of modelled distributions
• Stochastic PDEs, Regularity Structures, and Interacting Particle Systems