CONVERGENCE OF A SEQUENCE OF MARKOV CHAINSTO A DIFFUSION TYPE PROCESS

摘要

A random polygonal line constructed from a sequence of series of ho-mogeneous Markov chains is considered under rather nonregular dependence of theirlocal characteristics on a series number. Sufficient conditions are obtained for theweak convergence of a random polygonal line to a diffusion type process. The condi-tions are expressed explicitly in terms of local characteristics of the Markov chains.