Skip to Main content Skip to Navigation
Theses

Etude de la solution stationnaire de l'équation Y(n+1)=a(n)Y(n)+b(n) à coefficients aléatoires

Abstract : The linear autoregressive process (AR) in discrete time with random coefficients contains a large class of time series models that are very popular in statistics. Under weak assumptions, this process has a unique stationnary solution. The behaviour of its tail at infinity has been investigated by H. Kesten, E. LePage and C. Goldie when the coefficients are independent. This thesis extends their results in two directions. In a first part, we study the one-dimensionnal AR process with Markov switching introduced by J. D. Hamilton in econometrics. We get a similar result as in the independent case that can also be extended to continuous time processes. In a second part, we study the multidimensional model with independent coefficients. We extend the results mentionned above to a wider class of coefficients, namely a class with a property of irreducibility and proximality. Both parts make an intensive use of Renewal theory and Markovian operators.
Document type :
Theses
Complete list of metadatas

https://tel.archives-ouvertes.fr/tel-00007497
Contributor : Benoîte de Saporta <>
Submitted on : Tuesday, December 7, 2004 - 9:55:34 AM
Last modification on : Thursday, January 7, 2021 - 4:12:38 PM
Long-term archiving on: : Monday, September 20, 2010 - 12:04:51 PM

Identifiers

  • HAL Id : tel-00007497, version 2

Citation

Benoîte de Saporta. Etude de la solution stationnaire de l'équation Y(n+1)=a(n)Y(n)+b(n) à coefficients aléatoires. Mathématiques [math]. Université Rennes 1, 2004. Français. ⟨tel-00007497v2⟩

Share

Metrics

Record views

487

Files downloads

715