Artículos (Análisis Funcional)

URI permanente para esta colección

https://hdl.handle.net/10784/4395

Examinar

Examinando Artículos (Análisis Funcional) por Materia "ESPACIOS DE BANACH"

Mostrando 1 - 2 de 2
  • No hay miniatura disponible
    Ítem
    A q-exponential statistical Banach manifold
    (ELSEVIER, 2013-02) Quiceno Echavarría, Héctor Román; Loaiza Ossa, Gabriel Ignacio; department:Universidad EAFIT. Escuela de Ciencias. Grupo de Investigación Análisis Funcional y Aplicaciones; Héctor R. Quiceno (hquiceno@eafit.edu.co); Gabriel Loaiza (gloaiza@eafit.edu.co); Análisis Funcional y Aplicaciones
    Letµbe a given probability measure andMµ the set ofµ-equivalent strictly positive probability densities -- In this paper we construct a Banach manifold on Mµ, modeled on the space L∞(p · µ) where p is a reference density, for the non-parametric q-exponential statistical models (Tsallis’s deformed exponential), where 0 < q < 1 is any real number -- This family is characterized by the fact that when q → 1, then the non-parametric exponential models are obtained and the manifold constructed by Pistone and Sempi is recovered, up to continuous embeddings on the modeling space -- The coordinate mappings of the manifold are given in terms of Csiszár’s Φ-divergences; the tangent vectors are identified with the one-dimensional q-exponential models and q-deformations of the score function
  • No hay miniatura disponible
    Ítem
    A Riemannian geometry in the q-Exponential Banach manifold induced by q-Divergences
    (Springer Berlin Heidelberg, 2013) Loaiza Ossa, Gabriel Ignacio; Quiceno Echavarría, Héctor Román; Universidad EAFIT. Escuela de Ciencias. Grupo de Investigación Análisis Funcional y Aplicaciones; Gabriel Loaiza (gloaiza@eafit.edu.co); Héctor R. Quiceno (hquiceno@eafit.edu.co); Análisis Funcional y Aplicaciones
    For the family of non-parametric q-exponential statistical models, in a former paper, written by the same authors, a differentiable Banach manifold modelled on Lebesgue spaces of real random variables has been built -- In this paper, the geometry induced on this manifold is characterized by q-divergence functionals -- This geometry turns out to be a generalization of the geometry given by Fisher information metric and Levi-Civita connections -- Moreover, the classical Amari´s α-connections appears as special case of the q−connections (q) -- The main result is the expected one, namely the zero curvature of the manifold