Well-posedness of stochastic evolution equations with Hölder continuous noise
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866910371049111552 |
|---|---|
| author | Schmitz, Kerstin Zimmermann, Aleksandra |
| author_facet | Schmitz, Kerstin Zimmermann, Aleksandra |
| contents | We show existence and pathwise uniqueness of probabilistically strong solutions to a pseudomonotone stochastic evolution problem on a bounded domain $D\subseteq\mathbb{R}^d$, $d\in\mathbb{N}$, with homogeneous Dirichlet boundary conditions and random initial data $u_0\in L^2(Ω;L^2(D))$. The main novelty is the presence of a merely Hölder continuous multiplicative noise term. In order to show the well-posedness, we simultaneously regularize the Hölder noise term by inf-convolution and add a perturbation by a higher order operator to the equation. Using a stochastic compactness argument we may pass to the limit and we obtain first a martingale solution. Then by a pathwise uniqueness argument we get existence of a probabilistically strong solution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_11917 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Well-posedness of stochastic evolution equations with Hölder continuous noise Schmitz, Kerstin Zimmermann, Aleksandra Probability Analysis of PDEs 60H15, 35R60 We show existence and pathwise uniqueness of probabilistically strong solutions to a pseudomonotone stochastic evolution problem on a bounded domain $D\subseteq\mathbb{R}^d$, $d\in\mathbb{N}$, with homogeneous Dirichlet boundary conditions and random initial data $u_0\in L^2(Ω;L^2(D))$. The main novelty is the presence of a merely Hölder continuous multiplicative noise term. In order to show the well-posedness, we simultaneously regularize the Hölder noise term by inf-convolution and add a perturbation by a higher order operator to the equation. Using a stochastic compactness argument we may pass to the limit and we obtain first a martingale solution. Then by a pathwise uniqueness argument we get existence of a probabilistically strong solution. |
| title | Well-posedness of stochastic evolution equations with Hölder continuous noise |
| topic | Probability Analysis of PDEs 60H15, 35R60 |
| url | https://arxiv.org/abs/2403.11917 |