Uniform acceleration expansions for Markov chains with time-varying rates (Q1296718)

For time-inhomogeneous Markov chains with finite state space and continuous time, uniform acceleration (UA) expansion is constructed. The UA expansion is a special case of asymptotic approximation with its first term equal to the pointwise stationary approximation. Using the UA expansion the authors prove results that can be treated as analogous to the stationarity and ergodicity properties of homogeneous in time chains. As an example, time-varying birth-death process is considered. The accuracy of the approximation is illustrated by numerical calculations for (time-varying) Erlang loss model.