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arXiv · 1511.08888

Malliavin Calculus for regularity structures: the case of gPAM

Giuseppe Cannizzaro·Peter K. Friz·Paul Gassiat
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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 $L^2$-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.

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Giuseppe Cannizzaro, Peter K. Friz, Paul Gassiat. 2015-11-28. Malliavin Calculus for regularity structures: the case of gPAM. https://arxiv.org/abs/1511.08888

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