Ergodicity for stochastic T-monotone parabolic obstacle problems
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2023
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866912211929137152 |
|---|---|
| author | Tahraoui, Yassine |
| author_facet | Tahraoui, Yassine |
| contents | This work aims to investigate the existence of ergodic invariant measures and its uniqueness, associated with obstacle problems governed by a T-monotone operator defined on Sobolev spaces and driven by a multiplicative noise in a bounded domain of $\mathbb{R}^d$ with homogeneous boundary conditions. We show that the solution defines a Markov-Feller semigroup defined on the space of real bounded continuous functions of a convex subset related to the obstacle and we prove the existence of ergodic invariant measures and its uniqueness, under suitable assumptions. Our method relies on a combination of "Krylov Bogoliubov theorem", "Krein Milman theorem" and Lewy-Stampacchia inequalities to control the reflection measure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_02637 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Ergodicity for stochastic T-monotone parabolic obstacle problems Tahraoui, Yassine Probability Analysis of PDEs Dynamical Systems 35K86, 35R35, 47D07, 60H15 This work aims to investigate the existence of ergodic invariant measures and its uniqueness, associated with obstacle problems governed by a T-monotone operator defined on Sobolev spaces and driven by a multiplicative noise in a bounded domain of $\mathbb{R}^d$ with homogeneous boundary conditions. We show that the solution defines a Markov-Feller semigroup defined on the space of real bounded continuous functions of a convex subset related to the obstacle and we prove the existence of ergodic invariant measures and its uniqueness, under suitable assumptions. Our method relies on a combination of "Krylov Bogoliubov theorem", "Krein Milman theorem" and Lewy-Stampacchia inequalities to control the reflection measure. |
| title | Ergodicity for stochastic T-monotone parabolic obstacle problems |
| topic | Probability Analysis of PDEs Dynamical Systems 35K86, 35R35, 47D07, 60H15 |
| url | https://arxiv.org/abs/2311.02637 |