Multiple time scale decomposition of discrete time Markov chains (Q1111248)

The multiple time scale decomposition of discrete time, finite state Markov chains is addressed. In another paper by the same authors [J. Assoc. Comput. Mach. 35, No.3, 675-696 (1988; Zbl 0643.60057)], the behavior of a continuous time Markov chain is approximated using a fast time scale, \(\epsilon\)-independent, continuous time process, and a reduced order perturbed process. The procedure can then be iterated to obtain a complete multiple time scale decomposition. In the discrete time case presented in this paper, the basic approximation has a `hybrid' form. In this form, the fast time scale behavior is approximated using an \(\epsilon\)-independent discrete time Markov chain, and the slow behavior is captured by a perturbed, continuous time process.