On strong ergodicity for nonhomogeneous continuous-time Markov chains (Q1327551)

There are considered continuous-time Markov processes \(X(t)\), \(t>0\), and \(\overline{X}(t)\), \(t>0\), with countable state space. Assuming defined ergodicity properties of \(\overline{X}\) and using stability theorems of solutions of linear differential equations in \(l_ 1\)-space, the ergodicity properties of \(X\) are derived, when the intensity matrices for \(X\) and \(\overline{X}\) are close. Sharp estimates of the rates of convergence to the limit regimes are also obtained. Applications for some classes of birth and death processes are close.