A hierarchy in the family of real surjective functions

This expository paper focuses on the study of extreme surjective functions in ℝℝ. We present several different types of extreme surjectivity by providing examples and crucial properties. These examples help us to establish a hierarchy within the different classes of surjectivity we deal with. The classes presented here are: everywhere surjective functions, strongly everywhere surjective functions, κ-everywhere surjective functions, perfectly everywhere surjective functions and Jones functions. The algebraic structure of the sets of surjective functions we show here is studied using the concept of lineability. In the final sections of this work we also reveal unexpected connections between the different degrees of extreme surjectivity given above and other interesting sets of functions such as the space of additive mappings, the class of mappings with a dense graph, the class of Darboux functions and the class of Sierpiński-Zygmund functions in ℝℝ

Análisis wavelet de la precipitación en la Península Ibérica

Ponencia presentada en: II Congreso de la Asociación Española de Climatología “El tiempo del clima”, celebrado en Valencia del 7 al 9 de junio de 2001[ES]Se ha estudiado la variabilidad climática en la Península Ibérica mediante un análisis wavelet. El conjunto de datos está formado por series precipitación mensual de la Península Ibérica y las Islas Baleares. Aparecen diferencias no sólo en los análisis wavelet continuo y discreto, sino también los resultados son distintos para distintas zonas de la Península. Como consecuencia de esto se ha dividido el territorio peninsular en dos regiones: la región Atlántica y la región Mediterránea y se ha realizado el análisis continuo y discreto en ambas. Se pueden observar fuertes diferencias en la intensidad de los coeficientes wavelet en las dos regiones, así como en la variabilidad que muestran. En la región Mediterránea aparecen variaciones más intensas para grandes escalas temporales mientras que en la región Atlántica las escalas temporales más destacadas son más cortas. Estas características se observan tanto en el tratamiento discreto como en el continuo.[EN]Climate variability in the Iberian Peninsula has been analysed by means of a wavelet analysis. The dataset consists monthly totals precipitation including the Iberian Peninsula and Balearic Islands. Both continuous and discrete wavelet transforms have been applied in order to study different features of frequencies in the dataset. It can be observed several differences not only in both wavelet analyses but also in results of the Iberian zones. As these results, the study has been divided taking into account two different regions in Iberia: the atlantic and the mediterranean areas for both types of wavelet transforms. It can be noted strong differences between the variability intensities of wavelet coefficients in two separated areas. Thus, the intensity of variations is stronger in the Mediterranean areas than in Atlantic zones on shorter time-scales. These features have been observed in both continuous and discrete treatment.Este trabajo se ha desarrollado parcialmente mediante financiación del proyecto REN2000-0786/CLI

Internacionalización de los estudios de másteres en Matemáticas: un paso adelante

Fac. de Ciencias MatemáticasFALSEsubmitte

The invariant optimal sampling plan in a sequentially planned decision procedure

We define the invariant sequentially planned decision procedure under a group of measurable transformations. By means of a previous reduction of the problem, we obtain the optimal invariant sequentially planned decision procedure that minimizes the risk function. First we find the solution for the horizon with a maximal number of stages, based on the present information; later, the general case is solved but the solution is based on the past information. Finally, we study the possibility of approximating the general case by a sequence of truncated problems with a maximal number of stages, obtaining a solution based on the present informati

Procedimientos secuenciales generalizados

Los problemas de decisión secuencialmente planificados, son problemas secuenciales en los que en cada etapa no solo se decide si para o continuar con el muestreo, sino en este último caso cual es el tamaño muestral de la siguiente submuestra, y esta decisión se toma con la informacion disponible hasta ese instante. Esta memoria está estructurada en cuatro capítulos. El primero de ellos titulado Procedimientos de decisión secuencialmente planificados es un capítulo donde se exponen los elementos de los problemas de decisión secuencialmente planificados necesarios para el posterior desarrollo de la memoria. En el segundo capítulo titulado Análisis Estocastico se lleva a cabo un estudio de corte probabilístico sobre estos procesos, que tiene como objetivo demostrar el teorema de parada opcional para una sucesion de planes de muestreo creciente. En el tercer capítulo titulado Suficiencia se generaliza este concepto a los problemas de decisión secuencialmente planificados y se demuestra que la clase de reglas de decisión basadas en la familia suficiente transitiva forma una clase esencialmente completa. Y finalmente en el cuarto capítulo título Procedimientos de secuencialmente planificados invariantes, se generaliza el concepto de invariancia a estos problemas; se construye el plan de muestreo óptimo invariante que minimiza el riesgo asociado al problema y se aproxima el valor del problema general pro los valores de los problemas truncados en numero de etapas (se realizan dos aproximaciones). Se concluyen con las referencias bibliográficas empleada

The optional sampling theorem for submartingales in the sequentially planned context.

The optional sampling theorem is considered in the sequentially planned context. We prove the optional sampling theorem for direct successors and for sampling plans with a finite number of stages. Also, the theorem is studied in the general case under a uniform integrability condition; we obtain it for submartingales with a last element, and for submartingales that verify a bounded condition based on uniform integrability

Generalized p value for multivariate Gaussian stochastic processes in continuous time

We construct a Generalized p value for testing statistical hypotheses on the comparison of mean vectors in the sequential observation of two continuous time multidimensional Gaussian processes. The mean vectors depend linearly on two multidimensional parameters and with different conditions about their covariance structures. The invariance of the generalized p value considered is proved under certain linear transformations. We report results of a simulation study showing power and errors probabilities for them. Finally, we apply our results to a real data set

A hierarchy in the family of real surjective functions

This expository paper focuses on the study of extreme surjective functions in ℝℝ. We present several different types of extreme surjectivity by providing examples and crucial properties. These examples help us to establish a hierarchy within the different classes of surjectivity we deal with. The classes presented here are: everywhere surjective functions, strongly everywhere surjective functions, κ-everywhere surjective functions, perfectly everywhere surjective functions and Jones functions. The algebraic structure of the sets of surjective functions we show here is studied using the concept of lineability. In the final sections of this work we also reveal unexpected connections between the different degrees of extreme surjectivity given above and other interesting sets of functions such as the space of additive mappings, the class of mappings with a dense graph, the class of Darboux functions and the class of Sierpiński-Zygmund functions in ℝℝ

Modes of convergence of random variables and algebraic genericity

Important probabilistic problems require to find the limit of a sequence of random variables. However, this limit can be understood in different ways and various kinds of convergence can be defined. Among the many types of convergence of sequences of random variables, we can highlight, for example, that convergence in alternatives sense implies convergence in probability, which, in turn, implies convergence in distribution, besides that all these implications are strict. In this paper, the relationship between several types of convergence of sequences of random variables will be analyzed from the perspective of lineability theory.Depto. de Estadística e Investigación OperativaFac. de Ciencias MatemáticasInstituto de Matemática Interdisciplinar (IMI)TRUEpu

Sufficiency in sequentially planned decision procedures

Sampling plan, sequentially planned procedure, sufficient σ-fields, 62L10, 60G40,