Related papers: Central Limit Theorem for Symmetric Exchangeable R…
A central limit theorem is established for a sum of random variables belonging to a sequence of random fields. The fields are assumed to have zero mean conditional on the past history and to satisfy certain conditional $\alpha$-mixing…
We obtain the analogue of the classical result by Erd\"os and Kac on the limiting distribution of the maximum of partial sums for exchangeable random variables with zero mean and variance one. We show that, if the conditions of the central…
A non-classical formulation of the central limit theorem is given for sequences of independent random variables with finite second moments. Singular sequences whose members all have a degenerate or normal distribution are excluded from…
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…
General Central limit theorem deals with weak limits (in type) of sums of row-elements of array random variables. In some situations as in the invariance principle problem, the sums may include only parts of the row-elements. For strictly…
In this paper, we give the central limit theorem and almost sure central limit theorem for products of some partial sums of independent identically distributed random variables.
We prove a central limit theorem for a sequence of random variables whose means are ambiguous and vary in an unstructured way. Their joint distribution is described by a set of measures. The limit is (not the normal distribution and is)…
We study central limit theorems for certain nonlinear sequences of random variables. In particular, we prove the central limit theorems for the bounded conductivity of the random resistor networks on hierarchical lattices.
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…
This paper addresses the following classical question: giving a sequence of identically distributed random variables in the domain of attraction of a normal law, does the associated linear process satisfy the central limit theorem? We study…
A Central Limit Theorem is proved for linear random fields when sums are taken over finite disjoint union of rectangles. The approach does not rely upon the use of Beveridge Nelson decomposition and the conditions needed are similar to…
In this paper we investigate a sequence of square integrable random processes with space varying memory. We establish sufficient conditions for the central limit theorem in the space $L^2(\mu)$ for the partial sums of the sequence of random…
We prove a central limit theorem for the length of the longest subsequence of a random permutation which follows one of a class of repeating patterns. This class includes every fixed pattern of ups and downs having at least one of each,…
The Rotar central limit theorem is a remarkable theorem in the non-classical version since it does not use the condition of asymptotic infinitesimality for the independent individual summands, unlike the theorems named Lindeberg's and…
A finite range interacting particle system on a transitive graph is considered. Assuming that the dynamics and the initial measure are invariant, the normalized empirical distribution process converges in distribution to a centered…
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…
Recently a new type of central limit theorem for belief functions was given in Epstein et al. [9]. In this paper, we generalize the central limit theorem in Epstein et al. [9] to accommodate general bounded random variables. These results…
We prove a central limit theorem for linear triangular arrays under weak dependence conditions. Our result is then applied to the study of dependent random variables sampled by a $\bbZ$-valued transient random walk. This extends the results…
A central limit theorem is proved for some strictly stationary sequences of random variables that satisfy certain mixing conditions and are subjected to the "shrinking operators" $U_r(x):=[\max\{|x|-r,0\}]\cdot x/|x|,\ r \ge 0$. For…
We prove a central limit theorem for random walks with finite variance on linear groups.