Regeneration and general Markov chains. (1994)

• Record Type: Journal Article
• Authors: Kalashnikov, Vladimir V.
• Is Part Of: Journal of applied mathematics and stochastic analysis. Volume 7:Number 3(1994)
• Page Start: 357
• Page End: 371
• Publication Date: 1994
• Subjects: general Markov chain -- regenerative process -- ergodic theorem -- finite approximation -- test function -- rare event; Mathematical models -- Periodicals; Computer simulation -- Periodicals; Computer science -- Mathematics -- Periodicals; Computer science -- Mathematics; Computer simulation; Mathematical models; Applied Mathematics; Periodicals; Electronic journals; 519.22
• DOI: 10.1155/S1048953394000304
• Languages: English
• ISSNs: 1048-9533

Abstract

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.