Bratiichuk N. S.

We propose a new approach to the application of the Korolyuk potential method for the investigation of limit functionals for processes with independent increments. The formulas for the joint distribution of functionals related to crossing a level by the process are obtained and their asymptotic analysis is performed. The possibility of crossing a level by the process in a continuous way is also investigated.

A new approach is proposed for the investigation of the characteristics of queueing systems of the M/G/1/b-type with finite waiting rooms and a resume level of the input flow. A convenient algorithm is proposed for the numerical evaluation of stationary parameters of the system. Its efficiency is demonstrated for a specific system.

We consider a generalized Poisson process with reflection at the level T > 0. Under certain conditions on the distribution of the values of positive jumps of the process, we obtain representations for the characteristic functions of functionals associated with the exit of the indicated process to the negative semiaxis.

We present a brief survey of the main results obtained by V. S. Korolyuk in probability theory and mathematical statistics.

We investigate E ^θ/G/1/N-type queuing systems with limited queue. The investigation is based on the potential method proposed by Korolyuk

We extend the well-known results on canonical factorization for Markov additive processes with a finite Markov chain to the case where this chain is countable. We also formulate some corollaries of these results.