# Parabolic Anderson model on Heisenberg groups: the It\^o setting

@inproceedings{Baudoin2022ParabolicAM, title={Parabolic Anderson model on Heisenberg groups: the It\^o setting}, author={Fabrice Baudoin and Cheng Ouyang and Samy Tindel and Jing Wang}, year={2022} }

In this note we focus our attention on a stochastic heat equation defined on the Heisenberg group H of order n. This equation is written as ∂tu = 12∆u+ uẆα, where ∆ is the hypoelliptic Laplacian on H and {Ẇα;α > 0} is a family of Gaussian space-time noises which are white in time and have a covariance structure generated by (−∆)−α in space. Our aim is threefold: (i) Give a proper description of the noise Wα; (ii) Prove that one can solve the stochastic heat equation in the Itô sense as soon as…

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