Related papers: Limit Theorems for Random Sums of Random Summands

In this paper, we obtain an explicit total variation bound in the central limit theorem for the sums of non-i.i.d. random variables. Our results show that, under suitable assumptions, Lindeberg's condition is sufficient and necessary for…

Unlike classical simple random walks, one-dimensional random walks in random environments (RWRE) are known to have a wide array of potential limiting distributions. Under certain assumptions, however, it is known that CLT-like limiting…

Almost 10 years ago, Impagliazzo and Kabanets (2010) gave a new combinatorial proof of Chernoff's bound for sums of bounded independent random variables. Unlike previous methods, their proof is constructive. This means that it provides an…

We investigate the topologies of random geometric complexes built over random points sampled on Riemannian manifolds in the so-called "thermodynamic" regime. We prove the existence of universal limit laws for the topologies; namely, the…

We establish a central limit theorem for (a sequence of) multivariate martingales which dimension potentially grows with the length $n$ of the martingale. A consequence of the results are Gaussian couplings and a multiplier bootstrap for…

Recently a functional limit theorem for sums of moving averages with random coefficients and i.i.d. heavy tailed innovations has been obtained under the assumption that all partial sums of the series of coefficients are a.s. bounded between…

We derive a central limit theorem for the probability distribution of the sum of many critically correlated random variables. The theorem characterizes a variety of different processes sharing the same asymptotic form of anomalous scaling…

We prove a quenched functional central limit theorem (quenched FCLT) for the sums of a random field (r.f.) along a 2d-random walk in different situations: when the r.f. is iid with a second order moment (random sceneries), or when it is…

We develop large sample theory for merged data from multiple sources. Main statistical issues treated in this paper are (1) the same unit potentially appears in multiple datasets from overlapping data sources, (2) duplicated items are not…

This paper consists of a proof of a multivariate Central Limit Theorem for "rectangular" sums of dependent complex-valued, rho-prime-mixing random variables indexed by Z^d.

We study almost sure limiting behavior of extreme and intermediate order statistics arising from strictly stationary sequences. First, we provide sufficient dependence conditions under which these order statistics converges almost surely to…

In this paper we will prove various probabilistic limit theorems for some classes of distance expanding sequential dynamical systems (SDS). Our starting point here is certain sequential complex Ruelle-Perron-Frobenius (RPF) theorems which…

We prove the Simons-Johnson theorem for the sums $S_n$ of $m$-dependent random variables, with exponential weights and limiting compound Poisson distribution $\CP(s,\lambda)$. More precisely, we give sufficient conditions for…

In this paper, we investigate annealed and quenched limit theorems for random expanding dynamical systems. Making use of functional analytic techniques and more probabilistic arguments with martingales, we prove annealed versions of a…

Threshold-type counts based on multivariate occupancy models with log concave marginals admit bounded size biased couplings under weak conditions, leading to new concentration of measure results for random graphs, germ-grain models in…

In this paper, on the sublinear expectation space, we establish a comparison theorem between independent and convolutionary random vectors, which states that the partial sums of those two sequences of random vectors are identically…

We show that external randomization may enforce the convergence of test statistics to their limiting distributions in particular cases. This results in a sharper inference. Our approach is based on a central limit theorem for weighted sums.…

The theory of random matrices contains many central limit theorems. We have central limit theorems for eigenvalues statistics, for the log-determinant and log-permanent, for limiting distribution of individual eigenvalues in the bulk, and…

This article considers multivariate linear processes whose components are either short- or long-range dependent. The functional central limit theorems for the sample mean and the sample autocovariances for these processes are investigated,…

We prove upper and lower bounds on the effective content and logical strength for a variety of natural restrictions of Hindman's Finite Sums Theorem. For example, we show that Hindman's Theorem for sums of length at most 2 and 4 colors…