Weighted Besov spaces on Heisenberg groups and applications to the Parabolic Anderson model
Fuente:
arXiv
Salvato in:
| Autori principali: | , , , , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866915095152427008 |
|---|---|
| author | Baudoin, Fabrice Chen, Li Huang, Che-Hung Ouyang, Cheng Tindel, Samy Wang, Jing |
| author_facet | Baudoin, Fabrice Chen, Li Huang, Che-Hung Ouyang, Cheng Tindel, Samy Wang, Jing |
| contents | 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 $(-Δ)^{-α}$ 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 $\mathbf{H}_{n}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_04593 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Weighted Besov spaces on Heisenberg groups and applications to the Parabolic Anderson model Baudoin, Fabrice Chen, Li Huang, Che-Hung Ouyang, Cheng Tindel, Samy Wang, Jing Probability Functional Analysis 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 $(-Δ)^{-α}$ 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 $\mathbf{H}_{n}$. |
| title | Weighted Besov spaces on Heisenberg groups and applications to the Parabolic Anderson model |
| topic | Probability Functional Analysis |
| url | https://arxiv.org/abs/2501.04593 |