2019
Том 71
№ 11

# Volume 47, № 10, 1995

Article (Russian)

### Limit theorems in critical Galton-Watson branching processes with migration

Ukr. Mat. Zh. - 1995. - 47, № 10. - pp. 1307-1318

We study critical Galton-Watson branching processes with migration. It is assumed that the second moment of the number of direct descendants is infinite. Limit theorems are proved for the case where the mean value of migration is equal to zero. The work generalizes the results obtained by Nagaev and Khan [Teor. Veroyatn. Ee Primen.,25, No. 3, 523–534 (1980)] for the case where the second moment is finite.

Article (Ukrainian)

### Limit properties of the solutions of a Dirichlet problem in an elliptic domain

Ukr. Mat. Zh. - 1995. - 47, № 10. - pp. 1318–1327

We study solutions of a Dirichlet problem in a fixed ellipse and their behavior in the integral metric in the case where interior points approach the boundary of the ellipse.

Article (Russian)

### Recurrent relations for the solutions of an infinite system of linear algebraic equations

Ukr. Mat. Zh. - 1995. - 47, № 10. - pp. 1328–1332

We obtain recurrent relations for bounded solutions of the system of equations $$X_k - \sum\limits_{n = 0}^\infty {\frac{{(k + n)!}}{{k!n!}}} \alpha ^{k + n + 1} x_n = f_{k,} k = 0,1,..., \alpha \in (0,1/2),$$ with right-hand sides {f k } k=0 ={δ kj } k=0 ,j=0,1,..., where δ kj is the Kronecker symbol.

Article (Ukrainian)

### Some properties of random evolutions

Ukr. Mat. Zh. - 1995. - 47, № 10. - pp. 1333-1337

We study asymptotic properties of matrix-valued random evolutions and consider an example of evolutions of this type.

Anniversaries (Ukrainian)

### On the 60th birthday of Leonid Pavlovich Nizhnik

Ukr. Mat. Zh. - 1995. - 47, № 10. - pp. 1416–1417