Published in Lithuanian Mathematical Journal
We consider a discrete-time branching process in which the offspring distribution is generation-dependent and the number of reproductive individuals is controlled by a random mechanism. This model is a Markov chain, but, in general, the transition probabilities are nonstationary. Under not too restrictive hypotheses, this model presents the classic...
Published in Lithuanian Mathematical Journal
Abstract. We study an iterated temporal and contemporaneous aggregation of N independent copies of a strongly stationary subcritical Galton–Watson branching process with regularly varying immigration having index α ∈ (0 , 2). We show that limits of finite-dimensional distributions of appropriately centered and scaled aggregated partial-sum processe...
Published in Lithuanian Mathematical Journal
In this paper, we consider a strictly stationary sequence of m-dependent random variables through a compatible sequence of independent and identically distributed random variables by the moving averages processes. Using the Zolotarev distance, we estimate some rates of convergence in the weak limit theorems for normalized geometric random sums of t...
Published in Lithuanian Mathematical Journal
In the paper, we consider the partial-sum process ∑k=1ntXkn,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\sum}_{k=1}^{\left[ nt\right]}{X}_k^{(n)}, $$\end{document...
Published in Lithuanian Mathematical Journal
We study the distribution of the discriminant D(P) of polynomials P from the class Pn(Q) of all integer polynomials of degree n and height at most Q. We evaluate the asymptotic number of polynomials P ∈ Pn(Q) having all real roots and satisfying the inequality |D(P)| ≤ X as Q→∞and X/Q2n−2→ 0.
Published in Lithuanian Mathematical Journal
We prove that any beta distribution can be simulated by means of a sequence of distributions defined via multiplicative functions in a short interval.
Published in Lithuanian Mathematical Journal
Suppose that an algebraic number β of degree d = n(n − 1) over ℚ is expressible by the difference of two conjugate algebraic integers α1 ≠ α2 of degree n, namely, β = α1− α2. We prove that then there exists a constant c > 1, which depends on ∣α∣¯\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackag...
Published in Lithuanian Mathematical Journal
We consider simultaneous rational approximations to real and p-adic numbers. We prove that for any irrational number α0 and p-adic number α, there are infinitely many irreducible fractions satisfying ∣α0 − m/n ∣ 0 is an arbitrary number, and ∣ ⋅ ∣ p is the p-adic norm.
Published in Lithuanian Mathematical Journal
Bohr and Jessen proved the existence of a certain limit value regarded as the probability that values of the Riemann zeta function belong to a given region in the complex plane. They also studied the density of the probability, which has been called the M-function since the studies of Ihara and Matsumoto. In this paper, we construct M-functions for...
Published in Lithuanian Mathematical Journal
The triplet (a, b, c) of positive integers is said to be compositum-feasible if there exist number fields K and L of degrees a and b, respectively, such that the degree of their compositum KL equals c. We determine all compositum-feasible triplets (a, b, c) satisfying a ≤ b and b ∈ {8, 9}. This extends the classification of compositum-feasible trip...
