Gasanenko V. Ivestigation of random processes into tube domains

The dissertation is devoted to the investigation of functional of stay of random processes into domains which depend on the time. The total eхpansion of stay's functional is obtained for narrowing and expanding domains. The new results are obtained with respect to invariant sets for diffusion processes. It is proved the Doncker -- Prohorov's invariant principle with respect to curverline strips for increasing sums which are consructed by stationary sequence of random values with intermixing. The new exact formulas for sojurn probabolities of Wiener process are proved for domains which depend on the time. It is obtained the asymptotic of sojurn probabilities of Wiener process into such domains for large time. The new exat formulas of sojurn probabilities for time-depended domains are obtained for Wiener process.The exact formulas of sojurn probabilities of marked processes into monotone on time domains are obtained too. The limit theorems for raring processes are considered in the dissertation. It isproved new limit theorem about the approximation of raring processes by a renewall processes. This theorem is basic for proofs of limit theorems for the certain models of raring processes from biology, queueing theory, theory of indicators.