Abstract
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.