In this paper we consider the multivariate equation $X_{n+1} = A_{n+1}X_n + B_{n+1}$ with i.i.d. coefficients which have only a logarithmic moment. We give a necessary and sufficient condition for existence of a strictly stationary solution independent of the future. As an application we characterize the multivariate ARMA equations with general noise which have such a solution.
Publié le : 1992-10-14
Classification:
Autoregressive model,
linear stochastic system,
ARMA process,
strict stationarity,
state space system,
Lyapounov exponent,
stochastic difference equation,
60G10,
62M10,
60J10,
93E03
@article{1176989526,
author = {Bougerol, Philippe and Picard, Nico},
title = {Strict Stationarity of Generalized Autoregressive Processes},
journal = {Ann. Probab.},
volume = {20},
number = {4},
year = {1992},
pages = { 1714-1730},
language = {en},
url = {http://dml.mathdoc.fr/item/1176989526}
}
Bougerol, Philippe; Picard, Nico. Strict Stationarity of Generalized Autoregressive Processes. Ann. Probab., Tome 20 (1992) no. 4, pp. 1714-1730. http://gdmltest.u-ga.fr/item/1176989526/