Quasi-stationary distribution for the Langevin process in cylindrical domains, part I: existence, uniqueness and long-time convergence

Tony Lelièvre, Mouad Ramil, Julien Reygner

Consider the Langevin process, described by a vector (position,momentum) in ${\mathbb{R}}^d\times {\mathbb{R}}^d$. Let $\mathcal{O}$ be a ${\mathcal{C}}^2$ open bounded and connected set…