Related papers: Limit Theorems for Sums of p-Adic Random Variables

We discuss in detail the asymptotic distribution of sample expectiles. First, we show uniform consistency under the assumption of a finite mean. In case of a finite second moment, we show that for expectiles other then the mean, only the…

We consider sequences of random variables whose probability generating functions are polynomials all of whose roots lie on the unit circle. The distribution of such random variables has only been sporadically studied in the literature. We…

We derive the sharp non-asymptotical uniform estimations for tails of distributions for classical normed sums of centered normed independent random vectors having a moderate decreasing individual tails of summands.

In nature or societies, the power-law is present ubiquitously, and then it is important to investigate the mathematical characteristics of power-laws in the recent era of big data. In this paper we prove the superposition of non-identical…

When the distribution of a random (N) sum of independent copies of a r.v X is of the same type as that of X we say that X is N-sum stable. In this paper we consider a generalization of stability of geometric sums by studying distributions…

We obtain decay rates of probabilities of tails of polynomials in several independent random variables with heavy tails and derive stable limit theorems for nonconventional sums of such polynomials

The Central Limit Theorem states that, in the limit of a large number of terms, an appropriately scaled sum of independent random variables yields another random variable whose probability distribution tends to a stable distribution. The…

Let $E$ be a space of observables in a sequence of trials $\xi_n$ and define $m_n$ to be the empirical distributions of the outcomes. We discuss the almost sure convergence of the sequence $m_n$ in terms of the $\psi$-weak topology of…

This paper is part of series on self-contained papers in which a large part, if not the full extent, of the asymptotic limit theory of summands of independent random variables is exposed. Each paper of the series may be taken as review…

For a set of dependent random variables, without stationary or the strong mixing assumptions, we derive the asymptotic independence between their sums and maxima. Then we apply this result to high-dimensional testing problems, where we…

This paper studies the asymptotic properties of weighted sums of the form $Z_n=\sum_{i=1}^n a_i X_i$, in which $X_1, X_2, \ldots, X_n$ are i.i.d.~random variables and $a_1, a_2, \ldots, a_n$ correspond to either eigenvalues or singular…

In this paper we determine the distributional behavior of sums of free (in the sense of Voiculescu) identically distributed, infinitesimal random variables. The theory is shown to parallel the classical theory of independent random…

For noncorrelated random variables, we study a concentration property of the family of distributions of normalized sums formed by sequences of times of a given large length.

Convergence rate estimates in limit theorems for sums of independent random variables are considered.

Asymptotic expansions are derived for the tail distribution of the product of two correlated normal random variables with non-zero means and arbitrary variances, and more generally the sum of independent copies of such random variables.…

Non-standard distributional approximations have received considerable attention in recent years. They often provide more accurate approximations in small samples, and theoretical improvements in some cases. This paper shows that the…

Likelihood-based methods of statistical inference provide a useful general methodology that is appealing, as a straightforward asymptotic theory can be applied for their implementation. It is important to assess the relationships between…

In this note, we proved that weak limits, of sums of independent positive identically distributed random variables which are re-normalized by a non-linear shrinking transform $\max(0, x-r)$, are either degenerate or (some) compound Poisson…

We consider the continued fraction digits as random variables measured with respect to Lebesgue measure. The logarithmically scaled and normalized fluctuation process of the digit sums converges strongly distributional to a random variable…

Based on a new analytical approach to the definition of additive free convolution on probability measures on the real line we prove free analogs of limit theorems for sums for non-identically distributed random variables in classical…