Related papers: Tauberian and Abelian theorems for long-range depe…

In this study, we develop an asymptotic theory of nonparametric regression for locally stationary random fields (LSRFs) $\{{\bf X}_{{\bf s}, A_{n}}: {\bf s} \in R_{n} \}$ in $\mathbb{R}^{p}$ observed at irregularly spaced locations in…

Second-order characteristics including covariance and spectral density functions are fundamentally important for both statistical applications and theoretical analysis in functional time series. In the high-dimensional setting where the…

We derive the asymptotic distribution of ordinal-pattern frequencies under weak dependence conditions and investigate the long-run covariance matrix not only analytically for moving-average, Gaussian, and the novel generalized coin-tossing…

We consider random trigonometric polynomials with general dependent coefficients. We show that under mild hypotheses on the structure of dependence, the asymptotics as the degree goes to infinity of the expected number of real zeros…

The asymptotic results that underlie applications of extreme random fields often assume that the variables are located on a regular discrete grid, identified with $\mathbb{Z}^2$, and that they satisfy stationarity and isotropy conditions.…

The paper is devoted to the asymptotic behavior of value functions of abstract control problem with the long-time and discounted averages. The Uniform Tauberian Theorem for these problems states that the uniform convergence of value…

We characterize the quasiasymptotic behavior of distributions in terms of a Tauberian theorem for ridgelet transforms.

We study fluctuations in the number of zeros of random analytic functions given by a Taylor series whose coefficients are independent complex Gaussians. When the functions are entire, we find sharp bounds for the asymptotic growth rate of…

The spectral theory of semigroup generators is a crucial tool for analysing the asymptotic properties of operator semigroups. Typically, Tauberian theorems, such as the ABLV theorem, demand extensive information about the spectrum to derive…

We provide several Tauberian theorems for Laplace transforms with local pseudofunction boundary behavior. Our results generalize and improve various known versions of the Ingham-Fatou-Riesz theorem and the Wiener-Ikehara theorem. Using…

This paper introduces a version of empirical likelihood based on the periodogram and spectral estimating equations. This formulation handles dependent data through a data transformation (i.e., a Fourier transform) and is developed in terms…

In this paper we study the asymptotics of linear regression in settings with non-Gaussian covariates where the covariates exhibit a linear dependency structure, departing from the standard assumption of independence. We model the covariates…

We prove a topological version of abelian duality where the gauge groups are finite abelian. The theories are finite homotopy TFTs, topological analogues of the $p$-form $U(1)$ gauge theories. Using Brown-Comenetz duality, we extend the…

This paper investigates fractional Riesz-Bessel equations with random initial conditions. The spectra of these random initial conditions exhibit singularities both at zero frequency and at non-zero frequencies, which correspond to the cases…

The link between Tauberian theorems and large deviations is surveyed, with particular reference to regular variation.

We study the asymptotic behaviour of convolution-type functionals defined on general periodic domains by proving an extension theorem

Let X be a locally compact Abelian group. We consider linear forms of independent random variables with values in X. In doing so, one of the coefficients of the linear forms is a random variable with a Bernoulli distribution. For some…

We prove an invariance principle for Brownian motion in Gaussian or Poissonian random scenery by the method of characteristic functions. Annealed asymptotic limits are derived in all dimensions, with a focus on the case of dimension $d=2$,…

We study non-linear additive functionals of stationary Gaussian fields over anisotropically growing domains in $\mathbb{R}^d$, including spatiotemporal settings, and establish Gaussian and non-Gaussian limit theorems under non-separable…

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…