On limit distribution of the Matsumoto 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 multiple-particle continuous-time random walks.
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 Nonuniform Gaussian Approximation for Random Summation.
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 Shannon-McMillan's limit theorem for pairs of stationary random processes
On small deviations of Gaussian processes using majorizing measures
We give two examples of periodic Gaussian processes, having entropy numbers of exactly the same order but radically different small deviations. Our construction is based on Knopp's classical result yielding existence of continuous nowhere differentiable functions, and more precisely on Loud's functions. We also obtain a general lower bound for small deviations using the majorizing measure method. We show by examples that our bound is sharp. We also apply it to Gaussian independent sequences and...
On some limit distributions for geometric random sums
We define and give the various characterizations of a new subclass of geometrically infinitely divisible random variables. This subclass, called geometrically semistable, is given as the set of all these random variables which are the limits in distribution of geometric, weighted and shifted random sums. Introduced class is the extension of, considered until now, classes of geometrically stable [5] and geometrically strictly semistable random variables [10]. All the results can be straightforward...
On some sequences derived from the Poisson distribution.
On standard normal convergence of the multivariate Student -statistic for symmetric random vectors.
On the accuracy of approximation of the distribution of negative-binomial random sums by the gamma distribution
The main goal of this paper is to study the accuracy of approximation for the distributions of negative-binomial random sums of independent, identically distributed random variables by the gamma distribution.
On the approximation of an integral by a sum of random variables.