Rate of convergence to ergodic distribution for queue length in systems of the type <Emphasis Type="Italic">M</Emphasis><Superscript>θ</Superscript>/<Emphasis Type="Italic">G</Emphasis>/1/<Emphasis Type="Italic">N</Emphasis>

For finite-capacity queuing systems of the type M ^θ/G/1, convenient formulas for the ergodic distribution of the queue length are found, an estimate for the rate of convergence of the distribution of the queue length in the transient mode to the ergodic distribution is obtained, and computational algorithms for finding the rate of convergence are presented. __________ Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 9, pp. 1169–1178, September, 2007.     

Boundary-value problems for sums of random variables,defined on a countably-valued markov chain. II

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 41, No. 5, pp. 590–597, May, 1989.     

On the Creative Contribution of V. S. Korolyuk to the Development of Probability Theory

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

Size of the jump and behavior of the absolute maximum for processes with independent increments

For a process with independent increments and negative mean one investigates the asymptotic behavior of the distribution of the absolute maximum and the size of the jump over a positive level. Necessary and sufficient conditions for the existence of a proper distribution of the size of a jump over an infinite level are found.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 4, pp. 451–458, April, 1990.     

To the problem of canonical factorization for Markov additive processes

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.Published in Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 7, pp. 869–875, July, 1995.     

Boundary-value problems for sums of random variables,defined on a countably valued Markov chain. I

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 41, No. 2, pp. 139–146, February, 1989.     

Ruin problem for a generalized Poisson process with reflection

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. __________ Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 57, No. 11, pp. 1465–1475, November, 2005.