arXiv subjects

Elena Villa

Publications and source records attributed to Elena Villa.

7 recordsLinked to original sources

arXiv2026

Analysis of multivariate symbol statistics in primitive rational models

We study the asymptotic behaviour of sequences of multivariate random variables representing the number of occurrences of a given set of symbols in a word of length $n$ generated at random according to a rational stochastic model. Assuming primitive the matrix of the total weights of transitions of the model, we first determine asymptotic expressions for the mean values and the covariances of such statistics. Then we establish two asymptotic results that generalize known univariate cases to different regimes: a large deviation principle with speed $n$, implying almost sure convergence, and a multivariate Gaussian limit. Additionally, we introduce a novel moderate deviation result as a bridge between these regimes. Central to our proofs is a quasi-power property for the moment generating function of the statistics, allowing us to employ the G\"artner-Ellis Theorem for both large and moderate deviations.

math.PR↗

arXiv2023

A-BASE-DE-PROS: una implementación práctica de los Objetivos de Desarrollo Sostenible en la Universidad Politécnica de Madrid

The influence of the Sustainable Development Goals (SDGs) has been widely spread over the last years, establishing new public and privat policies. Education has also been experiencing this change by aligning with the previous goals. In this chapter, we briefly summarize the main activities conducted under the Grant APS22.2003 'Service-based learning of the SDGs related to a responsible production and consumption (A-BASE-DE-PROS)', which uses the SDG 12 as a guide line to raise the awareness of the importance of the 2030 Agenda among undergraduate and secondary-school students. In general, the service-based learning has increased the knowledge of the SDGs among the students. Furthermore, most of the (university and secondary) students found the service-learning

physics.ed-ph↗

arXiv2021

Asymptotic results for families of power series distributions

In this paper we consider suitable families of power series distributed random variables, and we study their asymptotic behavior in the fashion of large (and moderate) deviations. We also present two examples of fractional counting processes, where the normalizations of the involved power series distributions can be expressed in terms of the Prabhakar function. The first example allows to consider the counting process in \cite{PoganyTomovski}, the second one is inspired by a model studied in \cite{GarraOrsingherPolito}.

math.PR↗

arXiv2014

On the local approximation of mean densities of random closed sets

Mean density of lower dimensional random closed sets, as well as the mean boundary density of full dimensional random sets, and their estimation are of great interest in many real applications. Only partial results are available so far in current literature, under the assumption that the random set is either stationary, or it is a Boolean model, or it has convex grains. We consider here non-stationary random closed sets (not necessarily Boolean models), whose grains have to satisfy some general regularity conditions, extending previous results. We address the open problem posed in (Bernoulli 15 (2009) 1222-1242) about the approximation of the mean density of lower dimensional random sets by a pointwise limit, and to the open problem posed by Matheron in (Random Sets and Integral Geometry (1975) Wiley) about the existence (and its value) of the so-called specific area of full dimensional random closed sets. The relationship with the spherical contact distribution function, as well as some examples and applications are also discussed.

math.ST↗

arXiv2010

On the approximation of mean densities of random closed sets

Many real phenomena may be modelled as random closed sets in $\mathbb{R}^d$, of different Hausdorff dimensions. In many real applications, such as fiber processes and $n$-facets of random tessellations of dimension $n\leq d$ in spaces of dimension $d\geq1$, several problems are related to the estimation of such mean densities. In order to confront such problems in the general setting of spatially inhomogeneous processes, we suggest and analyze an approximation of mean densities for sufficiently regular random closed sets. We show how some known results in literature follow as particular cases. A series of examples throughout the paper are provided to illustrate various relevant situations.

math.ST↗

arXiv2008

A note on mean volume and surface densities for a class of birth-and-growth stochastic processes

Many real phenomena may be modelled as locally finite unions of $d$-dimensional time dependent random closed sets in $\mathbb{R}^d$, described by birth-and-growth stochastic processes, so that their mean volume and surface densities, as well as the so called mean \emph{extended} volume and surface densities, may be studied in terms of relevant quantities characterizing the process. We extend here known results in the Poissonian case to a wider class of birth-and-growth stochastic processes, proving in particular the absolute continuity of the random time of capture of a point $x\in\R^d$ by processes of this class.

math.PR↗

arXiv2008

Mean density of inhomogeneous Boolean models with lower dimensional typical grain

The mean density of a random closed set $Θ$ in $\R^d$ with Hausdorff dimension $n$ is the Radon-Nikodym derivative of the expected measure $\E[\h^n(Θ\cap\cdot)]$ induced by $Θ$ with respect to the usual $d$-dimensional Lebesgue measure. We consider here inhomogeneous Boolean models with lower dimensional typical grain. Under general regularity assumptions on the typical grain, related to the existence of its Minkowski content, and on the intensity measure of the underlying Poisson point process, we prove an explicit formula for the mean density. The proof of such formula provides as by-product estimators for the mean density in terms of the empirical capacity functional, which turns to be closely related to the well known random variable density estimation by histograms in the extreme case $n=0$. Particular cases and examples are also discussed.

math.PR↗