Journal of Applied Mathematics and Stochastic Analysis
Volume 7 (1994), Issue 3, Pages 357-371
Regeneration and general Markov chains
Institute of Systems Analysis, 9, Prospect 60 let Oktyabrya, Moscow 117312, Russia
Received 1 January 1994; Revised 1 May 1994
Copyright © 1994 Vladimir V. Kalashnikov. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Ergodicity, continuity, finite approximations and rare visits of
general Markov chains are investigated. The obtained results permit
further quantitative analysis of characteristics, such as, rates of
convergence, continuity (measured as a distance between perturbed and
non-perturbed characteristics), deviations between Markov chains, accuracy of approximations and bounds on the distribution function of the
first visit time to a chosen subset, etc. The underlying techniques use the
embedding of the general Markov chain into a wide sense regenerative
process with the help of splitting construction.