The goal of this note is to show how recent results on the theory of quasi-stationary distributions allow us to deduce general criteria for the geometric convergence of normalized unbounded semigroups.
"Practical criteria for $R$-positive recurrence of unbounded semigroups." Electron. Commun. Probab. 25 1 - 11, 2020. https://doi.org/10.1214/20-ECP288