Year: 2026
Type: article
Abstract: This work aims to investigate the existence of ergodic invariant measures and its uniqueness, associated with obstacle problems governed by a $$\textbf{T}$$ T -monotone operator defined on Sobolev spaces and driven by a multiplicative noise in a bounded domain of $$\mathbb {R}^d$$ 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.
Author: Yassine Tahraoui
Institution: Scuola Normale Superiore
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,190
OpenAlex ID: W7140760265