Related papers: Non-central limit theorem for non-linear functiona…

The subject of this work is the multivariate generalization of the theory of multiple Wiener--It\^o integrals. In the scalar valued case this theory was described in paper\cite{11}. Our proofs apply the technique of this work, but in the…

This is an extended version of a series of talks I held at the University of Bochum in 2017 about limit theorems for non-linear functionals of stationary Gaussian random fields. The goal of these talks was to give a fairly detailed…

This paper establishes a central limit theorem and an invariance principle for a wide class of stationary random fields under natural and easily verifiable conditions. More precisely, we deal with random fields of the form $X_k =…

We prove a nonconventional invariance principle (functional central limit theorem) for random fields.

In this paper, we study almost sure central limit theorems for sequences of functionals of general Gaussian fields. We apply our result to non-linear functions of stationary Gaussian sequences. We obtain almost sure central limit theorems…

The limit Gaussian distribution of multivariate weighted functionals of nonlinear transformations of Gaussian stationary processes, having multiple singular spectra, is derived, under very general conditions on the weight function. This…

We obtain an elementary invariance principle for multi-dimensional Brownian sheet where the underlying random fields are not necessarily independent or stationary. Possible applications include unit-root tests for spatial as well as panel…

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 focus on studying central limit theorems for functionals of some specific stationary random processes. In classical probability theory, it is well-known that for non-linear functionals of stationary Gaussian sequences, we…

In this paper we consider the asymptotic distributions of functionals of the sample covariance matrix and the sample mean vector obtained under the assumption that the matrix of observations has a matrix-variate location mixture of normal…

For an arbitrary integer N that is at least 2, this paper gives a construction of a strictly stationary, N-tuplewise independent sequence of (non-degenerate) bounded random variables such that the Central Limit Theorem fails to hold. The…

One reason why standard formulations of the central limit theorems are not applicable in high-dimensional and non-stationary regimes is the lack of a suitable limit object. Instead, suitable distributional approximations can be used, where…

This paper derives non-central asymptotic results for non-linear integral functionals of homogeneous isotropic Gaussian random fields defined on hypersurfaces in $\mathbb{R}^d$. We obtain the rate of convergence for these functionals. The…

The multivariate central limit theorems (CLT) for the volumes of excursion sets of stationary quasi-associated random fields on $\mathbb{R}^d$ are proved. Special attention is paid to Gaussian and shot noise fields. Formulae for the…

We present a general central limit theorem with simple, easy-to-check covariance-based sufficient conditions for triangular arrays of random vectors when all variables could be interdependent. The result is constructed from Stein's method,…

The central limit theorem is, with the strong law of large numbers, one of the two fundamental limit theorems in probability theory. Benjamin Jourdain and Alvin Tse have extended to non-linear functionals of the empirical measure of…

We establish a central limit theorem for the eigenvalue counting function of a matrix of real Gaussian random variables.

We establish a central limit theorem and an invariance principle for stationary random fields, with projective-type conditions. Our result is obtained via an m-dependent approximation method. As applications, we establish invariance…

We consider a borderline case: the central limit theorem for a strictly stationary time series with infinite variance but a Gaussian limit. In the iid case a well-known sufficient condition for this central limit theorem is regular…

We establish the central limit theorem for linear processes with dependent innovations including martingales and mixingale type of assumptions as defined in McLeish [Ann. Probab. 5 (1977) 616--621] and motivated by Gordin [Soviet Math.…