The ergodicity and stability of quasi-homogeneous Markov semigroups of operators

摘要

A nonhomogeneous-in-time semigroup of Markov operators acting in a Banach space is called quasi-homogeneous if the domain of its infinitesimal operator is dense and the operator itself can be represented as the sum of the infinitesimal operator of a homogeneous semigroup and a bounded operator function. Under the condition that the basic homogeneous semigroup is uniformly ergodic, we prove the uniform ergodicity and strong stability of the nonhomogeneous semigroup and obtain the estimates of the rate of convergence in the corresponding limit theorems.