# Harris-type results on geometric and subgeometric convergence to equilibrium for stochastic semigroups

@inproceedings{Caizo2021HarristypeRO, title={Harris-type results on geometric and subgeometric convergence to equilibrium for stochastic semigroups}, author={Jos{\'e} A. Ca{\~n}izo and St{\'e}phane Mischler}, year={2021} }

We provide simple and constructive proofs of Harris-type theorems on the existence and uniqueness of an equilibrium and the speed of equilibration of discretetime and continuous-time stochastic semigroups. Our results apply both to cases where the relaxation speed is exponential (also called geometric) and to those with no spectral gap, with non-exponential speeds (also called subgeometric). We give constructive estimates in the subgeometric case and discrete-time statements which seem both to…

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