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We provide simple and constructive proofs of Harris-type theorems on theexistence and uniqueness of an equilibrium and the speed of equilibration ofdiscrete-time and continuous-time stochastic semigroups. Our results apply bothto cases where the relaxation speed is exponential (also called geometric) andto those with no spectral gap, with non-exponential speeds (also calledsubgeometric). We give constructive estimates in the subgeometric case anddiscrete-time statements which seem both to be new. The method of proof alsodiffers from previous works, based on semigroup and interpolation arguments,valid for both geometric and subgeometric cases with essentially the sameideas. In particular, we present very simple new proofs of the geometric case.

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