Related papers: Edgeworth expansions for weakly dependent random v…

We give general conditions for the central limit theorem and weak convergence to Brownian motion (the weak invariance principle / functional central limit theorem) to hold for observables of compact group extensions of nonuniformly…

Let $\{X_i\}_{i=-\infty}^{\infty}$ be a sequence of random vectors and $Y_{in}=f_{in}(\mathcal{X}_{i,\ell})$ be zero mean block-variables where $\mathcal{X}_{i,\ell}=(X_i,...,X_{i+\ell-1}),i\geq 1$, are overlapping blocks of length $\ell$…

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…

A sum of observations derived by a simple random sampling design from a population of independent random variables is studied. A procedure finding a general term of Edgeworth asymptotic expansion is presented. The Lindeberg condition of…

We obtain the law of large numbers (LLN) and the central limit theorem (CLT) for weakly dependent non-stationary arrays of random fields with asymptotically unbounded moments. The weak dependence condition for arrays of random fields is…

The theory of dependency graphs is a powerful toolbox to prove asymptotic normality of sums of random variables. In this article, we introduce a more general notion of weighted dependency graphs and give normality criteria in this context.…

In this article, we study a class of lattice random variables in the domain of attraction of an $\alpha$-stable random variable with index $\alpha \in (0,2)$ which satisfy a truncated fractional Edgeworth expansion. Our results include…

Empirical processes for stationary, causal sequences are considered. We establish empirical central limit theorems for classes of indicators of left half lines, absolutely continuous functions and piecewise differentiable functions. Sample…

We consider a special class of weak dependent random variables with control on covariances of Lipschitz transformations. This class includes, but is not limited to, positively, negatively associated variables and a few other classes of…

Edgeworth expansions of first and second order are established for general linear rank statistics under the null hypothesis with asymptotically ''sufficiently'' small remainder terms. The methods used are the Stein method combined with an…

In this paper we present a conditional principle of Gibbs type for independent nonidentically distributed random vectors. We obtain this result by performing Edgeworth expansions for densities of sums of independent random vectors.

This paper investigates the asymptotic behavior of the extremes of a sequence of generalized Oppenheim random variables. Particularly, we establish conditions under which some normalized extremes of sequences arising from Oppenheim…

We obtain asymptotic expansions for probabilities $\mathbb{P}(S_N=k)$ of partial sums of uniformly bounded integer-valued functionals $S_N=\sum_{n=1}^N f_n(X_n)$ of uniformly elliptic inhomogeneous Markov chains. The expansions involve…

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.

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…

The aim of this paper is to study the asymptotic expansion in total variation in the Central Limit Theorem when the law of the basic random variable is locally lower-bounded by the Lebesgue measure (or equivalently, has an absolutely…

Central limit theorems are established for the sum, over a spatial region, of observations from a linear process on a $d$-dimensional lattice. This region need not be rectangular, but can be irregularly-shaped. Separate results are…

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…

For a branching process in random environment it is assumed that the offspring distribution of the individuals varies in a random fashion, independently from one generation to the other. Interestingly there is the possibility that the…

We prove quenched versions of (i) a large deviations principle (LDP), (ii) a central limit theorem (CLT), and (iii) a local central limit theorem (LCLT) for non-autonomous dynamical systems. A key advance is the extension of the spectral…