On limit distribution of the Riemann zeta-function
On limit properties of the reward from a Markov replacement process
On Lipschitz Dependence in Systems with Differentiated Inputs.
On maxima of waiting times
On m-dimensional stochastic processes in Banach spaces.
In the present paper the authors prove a weak law of large numbers for multidimensional processes of random elements by means of the random weighting. The results obtained generalize those of Padgett and Taylor.
On mean central limit theorems for stationary sequences
In this paper, we give estimates of the minimal distance between the distribution of the normalized partial sum and the limiting gaussian distribution for stationary sequences satisfying projective criteria in the style of Gordin or weak dependence conditions.
On mean values of subadditive processes
On Measures of Uniformly Distributed Sequences and Benford's Law.
On multiple-particle continuous-time random walks.
On Multivalued Amarts
In recent years, convergence results for multivalued functions have been developed and used in several areas of applied mathematics: mathematical economics, optimal control, mechanics, etc. The aim of this note is to give a criterion of almost sure convergence for multivalued asymptotic martingales (amarts). For every separable Banach space B the fact that every L¹-bounded B-valued martingale converges a.s. in norm to an integrable B-valued random variable (r.v.) is equivalent to the Radon-Nikodym...
On non-ergodic versions of limit theorems
The author investigates non ergodic versions of several well known limit theorems for strictly stationary processes. In some cases, the assumptions which are given with respect to general invariant measure, guarantee the validity of the theorem with respect to ergodic components of the measure. In other cases, the limit theorem can fail for all ergodic components, while for the original invariant measure it holds.
On nonperturbative localization with quasi-periodic potential.
On Nonuniform Gaussian Approximation for Random Summation.
On normal domination of (super)martingales.
On processes with conditional independent increments and stable convergence in law
On properties of binary random numbers
On Q-independence, limit theorems and q-Gaussian distribution
We formulate the notion of Q-independence which generalizes the classical independence of random variables and free independence introduced by Voiculescu. Here Q stands for a family of polynomials indexed by tiny partitions of finite sets. The analogs of the central limit theorem and Poisson limit theorem are proved. Moreover, it is shown that in some special cases this kind of independence leads to the q-probability theory of Bożejko and Speicher.
On random discrete distributions
On random split of the segment
We consider a partition of the interval [0,1] by two partition procedures. In the first a chosen piece of [0,1] is split into halves, in the second it is split by uniformly distributed points. Initially, the interval [0,1] is divided either into halves or by a uniformly distributed random variable. Next a piece to be split is chosen either with probability equal to its length or each piece is chosen with equal probability, and then the chosen piece is split by one of the above procedures. These...
On recurrence property of Riesz-Raikov sums.