Kavli Affiliate: Jing Wang
| First 5 Authors: Fabrice Baudoin, Li Chen, Che-Hung Huang, Cheng Ouyang, Samy Tindel
| Summary:
This article aims at a proper definition and resolution of the parabolic
Anderson model on Heisenberg groups $mathbf{H}_{n}$. This stochastic PDE is
understood in a pathwise (Stratonovich) sense. We consider a noise which is
smoother than white noise in time, with a spatial covariance function generated
by negative powers $(-Delta)^{-alpha}$ of the sub-Laplacian on
$mathbf{H}_{n}$. We give optimal conditions on the covariance function so that
the stochastic PDE is solvable. A large portion of the article is dedicated to
a detailed definition of weighted Besov spaces on $mathbf{H}_{n}$. This
definition, related paraproducts and heat flow smoothing properties, forms a
necessary step in the resolution of our main equation. It also appears to be
new and of independent interest. It relies on a recent approach, called
projective, to Fourier transforms on $mathbf{H}_{n}$.
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