相关论文: A Central Limit Theorem and Higher Order Results f…
We study the weak convergence (in the high-frequency limit) of the frequency components associated with Gaussian-subordinated, spherical and isotropic random fields. In particular, we provide conditions for asymptotic Gaussianity and we…
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…
Our main results are quantitative bounds in the multivariate normal approximation of centred subgraph counts in random graphs generated by a general graphon and independent vertex labels. We are interested in these statistics because they…
The purpose of this paper is to join two different threads of the recent literature on random fields on the sphere, namely the statistical analysis of higher order angular power spectra on one hand, and the construction of second-generation…
The paper is devoted to the investigation of Esscher's transform on high dimensional Euclidean spaces in the light of its application to the central limit theorem. With this tool, we explore necessary and sufficient conditions of normal…
An estimate of the order of approximation in the central limit theorem for strictly stationary associated random variables with finite moments of order q > 2 is obtained. A moderate deviation result is also obtained. We have a refinement of…
We characterize the angular polyspectra, of arbitrary order, associated with isotropic fields defined on the sphere S^2. Our techniques rely heavily on group representation theory, and specifically on the properties of Wigner matrices and…
In this paper, we introduce the concept of isotropic Hilbert-valued spherical random field, thus extending the notion of isotropic spherical random field to an infinite-dimensional setting. We then establish a spectral representation…
In this paper we study the asymptotic behavior of the angular bispectrum of spherical random fields. Here, the asymptotic theory is developed in the framework of fixed-radius fields, which are observed with increasing resolution as the…
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…
The field of analytic combinatorics is dedicated to the creation of effective techniques to study the large-scale behaviour of combinatorial objects. Although classical results in analytic combinatorics are mainly concerned with univariate…
In this paper, we establish a central limit theorem for a large class of general supercritical superprocesses with spatially dependent branching mechanisms satisfying a second moment condition. This central limit theorem generalizes and…
This paper provides quantitative Central Limit Theorems for nonlinear transforms of spherical random fields, in the high frequency limit. The sequences of fields that we consider are represented as smoothed averages of spherical Gaussian…
We give a central limit theorem, which has applications to Bayesian statistics and urn problems. The latter are investigated, by paying special attention to multicolor randomly reinforced generalized Polya urns.
We refine the classical Lindeberg-Feller central limit theorem by obtaining asymptotic bounds on the Kolmogorov distance, the Wasserstein distance, and the parametrized Prokhorov distances in terms of a Lindeberg index. We thus obtain more…
A particular case of degenerate Clebsch-Gordan coefficient can be expressed with three binomial coefficients. Such a formula, which may be obtained using the standard ladder operator procedure, can also be derived from the Racah-Shimpuku…
In this work we introduce the notion of an angular spectrum for a linear discrete time nonautonomous dynamical system. The angular spectrum comprises all accumulation points of longtime averages formed by maximal principal angles between…
We discuss the spectral asymptotics of some open subsets of the real line with random fractal boundary and of a random fractal, the continuum random tree. In the case of open subsets with random fractal boundary we establish the existence…
We provide rates of convergence in the central limit theorem in terms of projective criteria for adapted stationary sequences of centered random variables taking values in Banach spaces, with finite moment of order $p \in ]2,3]$ as soon as…
We obtain some sufficient conditions for the Central Limit Theorem for the random processes (fields) with values in the separable part of Holder space in the modern terms of majorizing (minorizing) measures, belonging to X.Fernique and…