# Yezhov I. I.

### Two-boundary problems for a random walk

Kadankov V. F., Kadankova T. V., Yezhov I. I.

Ukr. Mat. Zh. - 2007. - 59, № 11. - pp. 1485–1509

We solve main two-boundary problems for a random walk. The generating function of the joint distribution of the first exit time of a random walk from an interval and the value of the overshoot of the random walk over the boundary at exit time is determined. We also determine the generating function of the joint distribution of the first entrance time of a random walk to an interval and the value of the random walk at this time. The distributions of the supremum, infimum, and value of a random walk and the number of upward and downward crossings of an interval by a random walk are determined on a geometrically distributed time interval. We give examples of application of obtained results to a random walk with one-sided exponentially distributed jumps.

### System $G|G^κ|1$ with Batch Service of Calls

Ukr. Mat. Zh. - 2002. - 54, № 4. - pp. 447-465

For the queuing system *G*|*G* ^{κ}|1 with batch service of calls, we determine the distributions of the following characteristics: the length of a busy period, the queue length in transient and stationary modes of the queuing system, the total idle time of the queuing system, the output stream of served calls, etc.

### Main Probability Characteristics of the Queuing System $G^k|G|1$

Ukr. Mat. Zh. - 2001. - 53, № 10. - pp. 1343-1357

For the queuing system *G* ^{κ}|*G*|1 with batch arrivals of calls, we present the distributions of the following characteristics: the length of a busy period, queue length in transient and stationary modes of the queuing system, total idle time of the queuing system, virtual waiting time to the beginning of the service, input stream of calls, output stream of served calls, etc.

### Boundary Functionals for the Difference of Nonordinary Renewal Processes with Discrete Time

Ukr. Mat. Zh. - 2000. - 52, № 10. - pp. 1345-1356

For the difference of nonordinary renewal processes, we find the distribution of the main boundary functionals. For the queuing system *D* _{η} ^{δ} |*D* _{ξ} ^{κ} |1, we determine the distribution of the number of calls in transient and stationary modes.

### On the Distribution of the Number of Calls in the Queuing System $D_{η}|D_{ξ}^{\kappa}|1$

Ukr. Mat. Zh. - 2000. - 52, № 8. - pp. 1075-1081

For the queuing system *D* _{η}|*D* _{ξ} ^{k}|1, we determine the distribution of the number of calls in transient and stationary modes.

### On the generating function of the time of first hitting the boundary by a semicontinuous difference of independent renewal processes with discrete time

Ukr. Mat. Zh. - 2000. - 52, № 4. - pp. 553-561

For a semicontinuous difference of two independent renewal processes, we find the generating function of the time of first hitting the boundary.

### On the distribution of the maximum of the difference of independent renewal processes with discrete time

Ukr. Mat. Zh. - 1998. - 50, № 10. - pp. 1426–1432

We find the distribution of the maximum of the difference of two renewal processes with discrete time that is semicontinuous in discrete topology.

### Limit functionals for a semicontinuous difference of renewal processes with discrete time

Ukr. Mat. Zh. - 1993. - 45, № 12. - pp. 1710–1712

For a difference, semicontinuous in discrete topology, of two renewal processes with discrete time, the distribution of principal limit functionals is found.

### A modification of the branching process

Reshetnyak V. N., Yezhov I. I.

Ukr. Mat. Zh. - 1983. - 35, № 1. - pp. 31—36

### Some probability problems connected with prime numbers

Ukr. Mat. Zh. - 1981. - 33, № 6. - pp. 728-735

### On the distribution of the sequence of discards of a generalized Poisson process on a phase straight line

Ukr. Mat. Zh. - 1970. - 22, № 3. - pp. 355–360

### On the distribution of the size of a jump of given level for a sequence of maxima of random variables controlled by a Markov chain

Ukr. Mat. Zh. - 1969. - 21, № 6. - pp. 831–836

### An ergodic theorem for probabilistic processes with semi-markovian interference of chance

Ukr. Mat. Zh. - 1968. - 20, № 3. - pp. 384–387