Related papers: A quantitative averaging lemma for spatially depen…

Quantization of electromagnetic fields is investigated in the framework of stochastic variational method (SVM). Differently from the canonical quantization, this method does not require canonical form and quantization can be performed…

This paper develops a general asymptotic theory of local polynomial (LP) regression for spatial data observed at irregularly spaced locations in a sampling region $R_n \subset \mathbb{R}^d$. We adopt a stochastic sampling design that can…

We prove a global uniform Artin-Rees lemma type theorem for sections of ample line bundles over smooth projective varieties. This result is used to prove an Artin-Rees lemma for the polynomial ring with uniform degree bounds. The proof is…

We prove a generalization of the fundamental theorem of algebraic K-theory for Verdier-localizing functors by extending the proof for algebraic K-theory of spaces to the realm of stable $\infty$-categories. The formula behaves much better…

We propose a series-based nonparametric specification test for a regression function when data are spatially dependent, the `space' being of a general economic or social nature. Dependence can be parametric, parametric with increasing…

The surface area of a set which is only observed as a binary pixel image is often estimated by a weighted sum of pixel configurations counts. In this paper we examine these estimators in a design based setting -- we assume that the observed…

We consider a robust estimation of the mean vector for a sequence of i.i.d. observations in the domain of attraction of a stable law with different indices of stability, $DS(\alpha_1, \ldots, \alpha_p)$, such that $1<\alpha_{i}\leq 2$,…

We establish sufficient conditions for the asymptotic normality of kernel density estimators, applied to causal linear random fields. Our conditions on the coefficients of linear random fields are weaker than known results, although our…

Assuming the Generalized Riemann Hypothesis we obtain uniform, effective number-field analogues of Mertens' theorems.

This paper addresses the inference of spatial dependence in the context of a recently proposed framework. More specifically, the paper focuses on the estimation of model parameters for a class of generalized Gibbs random fields, i.e.,…

We consider a family of vector fields and we assume a horizontal regularity on their derivatives. We discuss the notion of commutator showing that different definitions agree. We apply our results to the proof of a ball-box theorem and…

Area-level models for small area estimation typically rely on areal random effects to shrink design-based direct estimates towards a model-based predictor. Incorporating the spatial dependence of the random effects into these models can…

We construct the space of vector fields on quantum groups . Its elements are products of the known left invariant vector fields with the elements of the quantum group itself. We also study the duality between vector fields and 1-forms. The…

In this paper, we consider the problem of testing the mean vector in the high dimensional settings. We proposed a new robust scalar transform invariant test based on spatial sign. The proposed test statistic is asymptotically normal under…

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…

A global real analytic regularity theorem for a quasilinear sum of squares of vector fields of Hormander rank 2 is given. A related local result for a special case was proved recently by the second author and L. Zanghirati in a paper titled…

This paper considers an estimation of semiparametric functional (varying)-coefficient quantile regression with spatial data. A general robust framework is developed that treats quantile regression for spatial data in a natural…

Using methods of Statistical Physics, we investigate the generalization performance of support vector machines (SVMs), which have been recently introduced as a general alternative to neural networks. For nonlinear classification rules, the…

In this article we review the construction of local, relativistic quantum vector fields by analytic continuation of Euclidean vector fields obtained as solutions of covariant SPDEs. We revise the formulation of such SPDEs by introducing new…

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…