On the asymptotic independence of Dirichlet series

The joint limit distribution of functions given by Dirichlet series is studied. The necessary and sufficient condition when this distribution is a product of marginal distributions is found. An example of such Dirichlet series with linear independent systems of exponents is presented. Partially supported by the Lithuanian State Science and Studies Foundation. Vilnius University, Naugarduko 24, 2006 Vilnius; Šiauliai University, P. Višinskio 25, 5419 Šiauliai, Lithuania. Translated from Lietuvos Matematikos Rinkinys, Vol. 39, No. 1, pp. 65–73, January–March, 1999. Translated by A. Laurinčikas     

An asymptotic formula of the Hellinger integral for renewal processes

Asymptotic formulas of the Hellinger integral are used in the investigation of properties of optimal estimates and statistical criteria. For a certain class of renewal processes, this formula was obtained by the author in [Lith. Math. J.,38(2), 131–143 (1998)]. In this paper, we obtain such a formula for all renewal processes whose intermediate renewal moments have absolutely continuous distributions. We use the traditional representation of the Hellinger integral and the theory of large deviations. Šiauliai University, Višinskio 25, 5400 Šiauliai, Lithuania. Translated from Lietuvos Matematikos Rinkinys, Vol. 39, No. 4, pp. 493–497, October–December, 1999. Translated by V. Mackevičius     

Some remarks on subfields of algebraic number fields

Vilnius University, Naugarduko 24, 2006 Vilnius, Lithuania. Translated from Lietuvos Matematikos Rinkinys, Vol. 35, No. 2 pp. 231–232, April–June, 1995     

Limit distributions of sums of random variables defined on a finite homogeneous Markov chain. II

Vilnius University, Naugarduko 24, 2600 Vilnius, Lithuania. Translated from Lietuvos Matematikos Rinkinys, Vol. 34, No. 1, pp. 94–106, January–March, 1994.     

On a problem of A. M. Vasil'ev

Vilnius Pedagogical University, Studentu 39, 2034 Vilnius, Lithuania. Translated from Lietuvos Matematikos Rinkinys, Vol. 34, No. 3, pp. 388–407, July–September, 1994.     

On the blow-up of solutions of a system of nonlinear Schrödinger equations

Vilnius University, Naugarduko 24, 2006 Vilnius, Lithuania. Translated from Lietuvos Matematikos Rinkinys, Vol. 35, No. 2, pp. 181–189, April–June, 1995.     

Difference scheme for the nonlinear problem of magnetization

Vilnius University, Naugarduko 24, 2006 Vilnius, Lithuania. Translated from Lietuvos Matematikos Rinkinys, Vol. 32, No. 2, pp. 237–248, April–June, 1992.     

Some estimates of thenth difference quotient of a function analytic in a convex region

Vilnius Technical University, Saulètekio 11, 2600 Vilnius, Lithuania. Translated from Lietuvos Matematikos Rinkinys, Vol. 35, No. 4, pp. 489–501, October–December, 1995.     

On the intrinsic normalizations of the seminonholonomic complexesSN Gr(m, n, (m+1)(n−m)−ϱ). I

Some intrinsic normalizations of seminonholonomic complexes of then-dimensional projective space are considered. Vilnius University, Naugarduko 24, 2006 Vilnius, Lithuania. Translated from Lietuvos Matematikos Rinkinys, Vol. 39, No. 4, pp. 517–538, October–December, 1999. Translated by R. Lapinskas     

Extended Euler-Maclaurin summation formulas

Vilnius Technical University, Saulétekio 11, 2600 Vilnius, Lithuania. Translated from Lietuvos Matematikos Rinkinys, Vol. 32, No. 2, pp. 249–260, April–June, 1992.     

Behavior of the homogeneous symmetric polynomial in an angular region

Vilnius Technical University, Saulétekio al. 11, 2600 Vilnius, Lithuania. Translated from Lietuvos Matematikos Rinkinys Vol. 35, No. 4, pp. 469–488, October–December, 1995.     

Intrinsic normalizations of a hyperplane distribution on the Grassmann manifold. I

We consider intrinsic normalizations of a hyperplane distribution on the Grassmann manifold of ann-dimensional projective space. Vilnius University, Naugarduko 24, 2600 Vilnius, Lithuania. Translated from Lietuvos Matematikos Rinkinys, Vol. 39, No. 2, pp. 257–273, April–June, 1999. Translated by V. Mackevičius     

Large deviations for integer centered poisson approximation

Large deviations in a centered Poisson approximation are examined. For lattice distributions, the centered Poisson approximation is more universal than the normal and standard Poisson laws. Vilnius University, Naugarduko 24, 2600 Vilnius, Lithuania. Translated from Lietuvos Matematikos Rinkinys, Vol. 39, No. 1, pp. 9–23, January–March, 1999. Translated by V. Čekanavičius     

The von mises theorem for farey fractions

We consider systems of strongly additive functions defined on the set of rational numbers and taking the values 0 and 1 on prime elements of ℚ. For these systems, we obtain necessary and sufficient conditions for the weak convergence to the Poisson law. Research supported by the Lithuanian State Science and Studies Foundation. Vilnius University, Naugarduko 24, 2600 Vilnius, Lithuania. Translated from Lietuvos Matematikos Rinkinys, Vol. 39, No. 3, pp. 425–439, July–September, 1999. Translated by J. <Siaulys     

Some estimates in theL p metric in the central limit theorem for additive functions

The convergence of the value distributions of a normalized sequence of strongly additive arithmetic functions to the standard normal law in theL _p metric is considered. An asymptotic formula for the variance is obtained. In both cases, the remainders are expressed in terms of the third absolute moment of the additive function. Vilnius University, Naugarduko 24, 2006 Vilnius, Lithuania. Translated from Lietuvos Matematikos Rinkinys, Vol. 39, No. 1, pp. 74–80, January–March, 1999. Translated by A. Mačiulis     

On approximation of stochastic differential equations with coefficients depending on the past

Vilnius University, Naugarduko 24, 2006 Vilnius, Lithuania. Published in Lietuvos Matematikos Rinkinys, Vol. 32, No. 2, pp. 285–298, April–June, 1992.     

The provability of certain sequents in additive arithmetic

Vilnius Pedagogical University, Studentų 39, 2034 Vilnius, Lithuania. Published in Lietuvos Matematikos Rinkinys, Vol. 35, No. 4, pp. 518–526, October–December, 1995.     

Compound transient phenomena in multiphase queuing systems. II

The paper continues the article by the author on functional limit theorems in queuing systems under heavy traffic. Theorems are proved for the virtual process of serving jobs when at phases of the queuing system various conditions of heavy traffic are satisfied (compound transient phenomena). Institute of Mathematics and Informatics, Akademijos 4, 2600 Vilnius, Lithuania. Translated from Lietuvos Matematikos Rinkinys, Vol. 39, No. 3, pp. 343–356, July–September, 1999. Translated by Z. Kryžius     

Stochastic processes with independent increments for random mappings

Using additive functions defined on the combinatorial structure of all mappings of anN set into itself, we define paths in the space endowed with the Skorokhod topology. Taking a mapping with equal probability, we get a sequence of random processes. Necessary and sufficient conditions for the weak convergence of this sequence to a stochastic process with independent increments are established. It is shown that the class of such processes contains all possible limits, provided that, on the components of a mapping, the additive functions have values small in average. Partially supported by the Lithuanian State Science and Studies Foundation. Vilnius University, Naugarduko 24, 2006 Vilnius, Lithuania. Translated from Lietuvos Matematikos Rinkinys, Vol. 39, No. 4, pp. 498–516, October–December, 1999. Translated by E. Manstavičius     

On weak convergence of random fields

We provide a characterization of compactness in the spaceD of functions of two variables defined on a unit square. The functions fromD have the property that their discontinuity points lie on smooth curves. Conditions for the tightness of probability measures inD and conditions for weak convergence of random fields with trajectories inD are derived. Vilnius Gediminas Technical University, Saulétekio 11; Institute of Mathematics and Informatics, Akademijos 4, 2600 Vilnius, Lithuania. Translated from Lietuvos Matematikos Rinkinys, Vol. 39, No. 2, pp 169–184, April–June, 1999. Translated by R. Banys