Regeneration and general Markov chains

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-pertrubed 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 embedded of the general Markov chain into a wide sense regenerative process with the help of splitting construction.