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arXiv · 0910.0315

Hypoellipticity in Infinite Dimensions

Martin Hairer
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Abstract

We consider semilinear parabolic stochastic PDEs driven by additive noise. The question addressed in this note is that of the regularity of transition probabilities. If the equation satisfies a Hormander 'bracket condition', then any finite-dimensional projection of the solution has a smooth density with respect to Lebesgue measure. One key ingredient in the argument is a bound on 'Wiener polynomials' that plays a role analogue to Norris' lemma.

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Martin Hairer. 2009-10-02. Hypoellipticity in Infinite Dimensions. https://arxiv.org/abs/0910.0315

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