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On the generalized Brascamp-Lieb-Barthe inequality, a Szego type limit theorem, and the asymptotic theory of random sums, integrals and
 

Summary: On the generalized Brascamp-Lieb-Barthe inequality, a Szeg¨o type limit
theorem, and the asymptotic theory of random sums, integrals and
quadratic forms
Florin Avram
Universit´e de Pau
Murad S. Taqqu
Boston University
March 6, 2005
Abstract
This paper describes a purely analytic approach for establishing central limit theorems for sums or
integrals tIT
Pm(Xt)dt and quadratic forms t,sIT
b(t - s)Pm,n(Xt, Xs)dsdt of Appell polynomials
Pm(Xt), Pm,n(Xt, Xs), where Xt is a linear process, that is, Xt = uRd a(t - u)du, t Rd
, where
t, t Rd
has stationary independent increments. We review known results and outline some open
problems related to this approach.
1 Introduction
1. Time series motivation. One-dimensional discrete time series with long memory have been ex-

  

Source: Avram, Florin - Laboratoire de Mathématiques Appliquées, Université de Pau et des Pays de l'Adour

 

Collections: Mathematics