We consider an autoregressive model on ℝ defined by the recurrence equation Xn=AnXn−1+Bn, where {(Bn, An)} are i.i.d. random variables valued in ℝ×ℝ+ and $\mathbb{E}[\log A_{1}]=0$ (critical case). It was proved by Babillot, Bougerol and Elie that there exists a unique invariant Radon measure of the process {Xn}. The aim of the paper is to investigate its behavior at infinity. We describe also stationary measures of two other stochastic recursions, including one arising in queuing theory.
Publié le : 2007-08-14
Classification:
Random coefficients autoregressive model,
affine group,
random equations,
queues,
contractive system,
regular variation,
60J10,
60B15,
60G50
@article{1186755239,
author = {Buraczewski, Dariusz},
title = {On invariant measures of stochastic recursions in a critical case},
journal = {Ann. Appl. Probab.},
volume = {17},
number = {1},
year = {2007},
pages = { 1245-1272},
language = {en},
url = {http://dml.mathdoc.fr/item/1186755239}
}
Buraczewski, Dariusz. On invariant measures of stochastic recursions in a critical case. Ann. Appl. Probab., Tome 17 (2007) no. 1, pp. 1245-1272. http://gdmltest.u-ga.fr/item/1186755239/