Yershov A. Limit theorems for random polygonal lines

The thesis concerns investigation of limit behavior of random polygonal lines constructed by series of random variables with local characteristics that depend on the number of series rather irregularly. Conditions under which random polygonal lines that are constructed by homogeneous Markov chains converge weakly to the diffusion type processes were obtained. The limit behavior of integral type functionals of homogeneous Markov chains was investigated. In the multidimensional case the conditions, under which given sets are stable for the series of random polygonal lines that are built by series of homogeneous Markov chains with local characteristics that could degenerate in limit, were obtained.