2009/10/02 by Martin Hairer, Hairer, Martin
Economics, Econometrics and Finance · Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Dynamics and Fractals #Probability (math.PR) #Stochastic processes and financial applications #math.AP #math.PR
paper · pdf · doi:10.48550/arxiv.0910.0315
ISAAC 09 conference proceedings
arxiv created 2009/10/02 · openalex publication_date 2009/10/02 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.