This work is concerned with aggregations in a singularly perturbed
Markov chain having a finite state space and fast and slow motions.The state
space of the underlying Markov chain can be decomposed into several groups of
recurrent states and a group of transient states.The asymptotic properties are
studied through sequences of unscaled and scaled occupation measures.By
treating the states within each recurrent class as a single state, an
aggregated process is defined and shown to be convergent to a limit Markov
chain.In addition, it is shown that a sequence of suitably rescaled occupation
measures converges to a switching diffusion process weakly.
@article{1019487355,
author = {Yin, G. and Zhang, Q. and Badowski, G.},
title = {Asymptotic properties of a singularly perturbed Markov chain with
inclusion of transient states},
journal = {Ann. Appl. Probab.},
volume = {10},
number = {2},
year = {2000},
pages = { 549-572},
language = {en},
url = {http://dml.mathdoc.fr/item/1019487355}
}
Yin, G.; Zhang, Q.; Badowski, G. Asymptotic properties of a singularly perturbed Markov chain with
inclusion of transient states. Ann. Appl. Probab., Tome 10 (2000) no. 2, pp. 549-572. http://gdmltest.u-ga.fr/item/1019487355/