Hypoellipticity in Infinite Dimensions

Details Hypoellipticity in Infinite Dimensions Hypoellipticity in Infinite Dimensions

2009-10-02

arxiv.org/abs/0910.0315v1

Mathematics

Probability

ISAAC 09 conference proceedings

Scientific paper

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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