Uniform acceleration expansions for Markov chains with time-varying rates

We study uniform acceleration (UA) expansions of finite-state continuous-ti me Markov chains with time-varying transition rates. The UA expansions can be used to justify evaluate and reline the pointwise stationary approximati on, which is the steady-state distribution associated with the time-depende nt generator at the time of interest. We obtain UA approximations from thes e UA asymptotic expansions. We derive a time-varying analog to the uniformi zation representation of transition probabilities for chains with constant transition rates, and apply it to establish asymptotic results related to t he UA asymptotic expansion. These asymptotic results can serve as appropria te time-varying analogs to the notions of stationary distributions and limi ting distributions. We illustrate the UA approximations by doing a numerica l example far the time-varying Erlang loss model.