Related papers: Tauberian and Abelian theorems for long-range depe…
Long-range dependent random fields with spectral densities which are unbounded at some frequencies are investigated. We demonstrate new examples of covariance functions which do not exhibit regular varying asymptotic behaviour at infinity.…
This paper is a short overview of the main Abelian- and Tauberian-type results from [4, 14, 26] regarding the asymptotic analysis of different classes of generalized functions in terms of appropriate frames. The Tauberian-type results…
Abel-Tauberian theorems relate power law behavior of distributions and their transforms. We formulate and prove a multivariate version for non-standard regularly varying measures on $\mathbb{R}_+^p$ and then apply it to prove that the joint…
This paper aims to explore the quasiasymptotic behavior of distributions through the fractional Hankel transform. We present Tauberian result that connects the asymptotic behavior of generalized functions in the Zemanian space with the…
The paper deals with the long-term behavior of positive operator semigroups on spaces of bounded functions and of signed measures, which have applications to parabolic equations with unbounded coefficients and to stochastic analysis. The…
The paper studies the asymptotic behaviour of weighted functionals of long-range dependent data over increasing observation windows. Various important statistics, including sample means, high order moments, occupation measures can be given…
The paper proves the Strong Law of Large Numbers for integral functionals of random fields with unboundedly increasing covariances. The case of functional data and increasing domain asymptotics is studied. Conditions to guarantee that the…
This paper investigates asymptotic properties of multifractal products of random fields. The obtained limit theorems provide sufficient conditions for the convergence of cumulative fields in the spaces $L_q.$ New results on the rate of…
In the paper we consider Lamperti type theorems for random fields. Together with known results we present some new results on ${\mathbb R}^m$-valued self-similar fields $\{{\bf X} ({\bf t}), \ {\bf t} \in {\mathbb R}^d \}$, their domains of…
Limit theorems are proved for quadratic forms of Gaussian random fields in presence of long memory. We obtain a non central limit theorem under a minimal integrability condition, which allows isotropic and anisotropic models. We apply our…
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…
In this paper we study the asymptotic theory for spectral analysis of stationary random fields, including linear and nonlinear fields. Asymptotic properties of Fourier coefficients and periodograms, including limiting distributions of…
This paper considers the asymptotic behaviour of volumes of excursion sets of subordinated Gaussian random fields with (possibly) infinite variance. Actually, we consider integral functionals of such fields and obtain their limiting…
We provide asymptotic results for the distribution of weighted nonlinear functionals of Gaussian field with long-range dependence. We also show that integral functionals and the corresponding additive functionals have same distributions…
Random fields play a central role in the analysis of spatially correlated data and, as a result, have a significant impact on a broad array of scientific applications. This paper studies the cepstral random field model, providing recursive…
For expansions in one-dimensional conformal blocks, we provide a rigorous link between the asymptotics of the spectral density of exchanged primaries and the leading singularity in the crossed channel. Our result has a direct application to…
We derive bilateral asymptotic as well as non-asymptotic estimates for the multivariate Laplace integrals. Possible applications: Tauberian theorems for random vectors.
This paper proposes a variational principle for the solutions of quantum field theories in which the ``trial functions'' are chosen from the algebra of asymptotic fields, and illustrates this variational principle in simple cases.
The paper investigates isotropic random fields for which the spectral density is unbounded at some frequencies. Limit theorems for weighted functionals of these random fields are established. It is shown that for a wide class of…
We study asymptotics of integrals of certain rational functions that depend on parameters in a field $K$ of characteristic zero. We use formal power series to represent the integral and prove certain identities about its coefficients…