Related papers: Limit Theorems for Random Sums of Random Summands
The paper is a sketch of systematic presentation of distributional limit theorems and their refinements for compound sums. When analyzing, e.g., ergodic semi-Markov systems with discrete or continuous time, this allows us to separate those…
In this paper, we study the fluctuations of sums of random variables with distribution defined as a mixture of light-tail and truncated heavy-tail distributions. We focus on the case when both the mixing coefficient and the truncation level…
This paper proves several weak limit theorems for the joint version of extreme order statistics and partial sums of independently and identically distributed random variables. The results are also extended to almost sure limit version.
The problem of convergence in law of normed sums of exchangeable random variables is examined. First, the problem is studied w.r.t. arrays of exchangeable random variables, and the special role played by mixtures of products of stable laws…
We derive new bounds of the remainder in a combinatorial central limit theorem without assumptions on independence and existence of moments of summands. For independent random variables our theorems imply Esseen and Berry-Esseen type…
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…
We consider a finite sequence of random points in a finite domain of a finite-dimensional Euclidean space. The points are sequentially allocated in the domain according to a model of cooperative sequential adsorption. The main peculiarity…
In this paper, we establish a local limit theorem for linear fields of random variables constructed from independent and identically distributed innovations each with finite second moment. When the coefficients are absolutely summable we do…
We generalise the Erdos-Renyi limit theorem on the maximum of the partial sums of random variables to the case when the number of terms in these sums is randomly distributed. Certain relations between the limiting theorems of this type and…
Limit theorems of strong law of large numbers and central limit theorem types are obtained for the compositions of independent identically distributed random unitary channels.
Lower and upper bounds are explored for the uniform (Kolmogorov) and $L^2$-distances between the distributions of weighted sums of dependent summands and the normal law. The results are illustrated for several classes of random variables…
We consider a variant of the randomly reinforced urn where more balls can be simultaneously drawn out and balls of different colors can be simultaneously added. More precisely, at each time-step, the conditional distribution of the number…
Multivariate distributions are explored using the joint distributions of marginal sample quantiles. Limit theory for the mean of a function of order statistics is presented. The results include a multivariate central limit theorem and a…
We present some product representations for random variables with the Linnik, Mittag-Leffler and Weibull distributions and establish the relationship between the mixing distributions in these representations. Based on these representations,…
Estimates are constructed for the deviation of the concentration functions of sums of independent random variables with finite variances from the folded normal distribution function without any assumptions concerning the existence of the…
Since the appearance of H. Robbins article (1948), the central limit theorems for random sums have been studied for about 70 years. The central limit theorems for random sums of independent random variables play a very important role in…
In this paper, we prove a conditional limit theorem for independent not necessarily identically distributed random variables. Namely, we obtain the asymptotic distribution of a large number of them given the sum.
This paper establishes a combinatorial central limit theorem for stratified randomization, which holds under a Lindeberg-type condition. The theorem allows for an arbitrary number or sizes of strata, with the sole requirement being that…
We consider the problem of bounding large deviations for non-i.i.d. random variables that are allowed to have arbitrary dependencies. Previous works typically assumed a specific dependence structure, namely the existence of independent…
We derive theorems which outline explicit mechanisms by which anomalous scaling for the probability density function of the sum of many correlated random variables asymptotically prevails. The results characterize general anomalous scaling…