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Cosmological local observables are at best statistically determined by the fundamental theory describing inflation. When the scalar inflaton is coupled uniformly to a collection of subdominant massless gauge vectors, rotational invariance…
We explore the notion of spatial extent and structure, already alluded to in earlier literature, within the formulation of quantum mechanics on the noncommutative plane. Introducing the notion of average position and its measurement, we…
In this paper we define (empirical) quadratic variations for a Gaussian isotropic random field $f$ on a unit sphere as sums over equidistant increments on one single geodesic line on the surface of the sphere. We prove a noncentral limit…
In the special theory of relativity, Lorentz invariance is extended in Minkowski spacetime from ideal inertial observers to actual observers by means of the hypothesis of locality, which postulates that accelerated observers are always…
This paper presents a central limit theorem for a pre-averaged version of the realized covariance estimator for the quadratic covariation of a discretely observed semimartingale with noise. The semimartingale possibly has jumps, while the…
In this article, we primarily propose a novel Bayesian characterization of stationary and nonstationary stochastic processes. In practice, this theory aims to distinguish between global stationarity and nonstationarity for both parametric…
This article presents a neural network approach for estimating the covariance function of spatial Gaussian random fields defined in a portion of the Euclidean plane. Our proposal builds upon recent contributions, expanding from the purely…
Multivariate spatial-statistical models are often used when modeling environmental and socio-demographic processes. The most commonly used models for multivariate spatial covariances assume both stationarity and symmetry for the…
We address the challenge of estimation in the context of constant linear effect models with dense functional responses. In this framework, the conditional expectation of the response curve is represented by a linear combination of…
In earlier work, using the light cone picture, a world sheet field theory that sums planar phi^3 graphs was constructed and developed. Since this theory is both non-local and not explicitly Lorentz invariant, it is desirable to have a…
In this paper, we observe a fixed number of unknown $2\pi$-periodic functions differing from each other by both phases and amplitude. This semiparametric model appears in literature under the name "shape invariant model." While the common…
The convergence properties of the stationary Fokker-Planck algorithm for the estimation of the asymptotic density of stochastic search processes is studied. Theoretical and empirical arguments for the characterization of convergence of the…
Correlated random fields are a common way to model dependence struc- tures in high-dimensional data, especially for data collected in imaging. One important parameter characterizing the degree of dependence is the asymp- totic variance…
Statistical inference for stochastic processes with time-varying spectral characteristics has received considerable attention in recent decades. We develop a nonparametric test for stationarity against the alternative of a smoothly…
It is well known that general relativity (GR) does not possess any non-trivial local (in a precise standard sense) and diffeomorphism invariant observables. We propose a generalized notion of local observables, which retain the most…
In this study, we develop an asymptotic theory of nonparametric regression for a locally stationary functional time series. First, we introduce the notion of a locally stationary functional time series (LSFTS) that takes values in a…
This paper addresses the estimation of locally stationary long-range dependent processes, a methodology that allows the statistical analysis of time series data exhibiting both nonstationarity and strong dependency. A time-varying…
Networked systems usually face different random uncertainties that make the performance of the least-squares (LS) linear filter decline significantly. For this reason, great attention has been paid to the search for other kinds of…
We study the properties of a stochastic heat equation with a generalized mixed fractional Brownian noise. We obtain the covariance structure, stationarity and obtain bounds for the asymptotic behaviour of the solution. We suggest estimators…
A new bivariate partial sum process for locally stationary time series is introduced and its weak convergence to a Brownian sheet is established. This construction enables the development of a novel self-normalized CUSUM test statistic for…