Ai. Zeifman et Dl. Isaacson, ON STRONG ERGODICITY FOR NONHOMOGENEOUS CONTINUOUS-TIME MARKOV-CHAINS, Stochastic processes and their applications, 50(2), 1994, pp. 263-273
Let X(t) be a nonhomogeneous continuous-time Markov chain. Suppose tha
t the intensity matrices of X(t) and some weakly or strongly ergodic M
arkov chain X(t)BAR are close. Some sufficient conditions for weak and
strong ergodicity of X(t) are given and estimates of the rate of conv
ergence are proved. Queue-length for a birth and death process in the
case of asymptotically proportional intensities is considered as an ex
ample.