Kartashov I. Limit theorems for difference additive functionals of Markov chains

Dissertiation concerns studies of limit behavior of difference additive functionals of Markov chains. The result which states that convergence of d.a.f to continuous functionals of Markov process in terms of uniform or local convergence of corresponding objects: expectations (characteristics) or "symbols" of functionals is obtained. Limit theorems are proved, particularly for cases where invariance principle fails, local time at point does not exist or characteristics of limit functional is discontinuous. Theorems regarding гniform convergence of families of functionals is proved.