We study uniform acceleration (UA) expansions of finite-state
continuous-time Markov chains with time-varying transition rates. The UA
expansions can be used to justify, evaluate and refine the pointwise stationary
approximation, which is the steady-state distribution associated with the
time-dependent generator at the time of interest. We obtain UA approximations
from these UA asymptotic expansions. We derive a time-varying analog to the
uniformization representation of transition probabilities for chains with
constant transition rates, and apply it to establish asymptotic results related
to the UA asymptotic expansion. These asymptotic results can serve as
appropriate time-varying analogs to the notions of stationary distributions and
limiting distributions. We illustrate the UA approximations by doing a
numerical example for the time-varying Erlang loss model.
@article{1028903375,
author = {Massey, William A. and Whitt, Ward},
title = {Uniform acceleration expansions for Markov chains with
time-varying rates},
journal = {Ann. Appl. Probab.},
volume = {8},
number = {1},
year = {1998},
pages = { 1130-1155},
language = {en},
url = {http://dml.mathdoc.fr/item/1028903375}
}
Massey, William A.; Whitt, Ward. Uniform acceleration expansions for Markov chains with
time-varying rates. Ann. Appl. Probab., Tome 8 (1998) no. 1, pp. 1130-1155. http://gdmltest.u-ga.fr/item/1028903375/