We develop the theory of invariant random fields in vector bundles. The spectral decomposition of an invariant random field in a homogeneous vector bundle generated by an induced representation of a compact connected Lie group G is obtained. We discuss an application to the theory of relic radiation, where G = SO(3). A theorem about equivalence of two different groups of assumptions in cosmological theories is proved.
Ce travail est une étude théorique d’opérateurs de Toeplitz dont le symbole est une fonction matricielle régulière définie positive partout sur le tore à une dimension. Nous proposons d’abord une formule d’inversion exacte pour un opérateur de Toeplitz à symbole matriciel, démontrée au moyen d’un théorème établi en annexe et donnant la solution du problème de la prédiction relatif à un passé fini pour un processus stationnaire du second ordre. Nous établissons ensuite, à partir de cet inverse, un...
In the context of high frequency data, one often has to deal with observations occurring at irregularly spaced times, at transaction times for example in finance. Here we examine how the estimation of the squared or other powers of the volatility is affected by irregularly spaced data. The emphasis is on the kind of assumptions on the sampling scheme which allow to provide consistent estimators, together with an associated central limit theorem, and especially when the sampling scheme depends on...
In this paper we apply techniques of spherical harmonic analysis to prove a local limit theorem, a rate of escape theorem, and a central limit theorem for isotropic random walks on arbitrary thick regular affine buildings of irreducible type. This generalises results of Cartwright and Woess where buildings are studied, Lindlbauer and Voit where buildings are studied, and Sawyer where homogeneous trees are studied (these are buildings).
Models of random sets and of point processes are introduced to simulate some specific clustering of points, namely on random lines in and and on random planes in . The corresponding point processes are special cases of Cox processes. The generating distribution function of the probability distribution of the number of points in a convex set and the Choquet capacity are given. A possible application is to model point defects in materials with some degree of alignment. Theoretical results...