On the invariant measure of the random difference equation $X_n=A_n X_{n-1}+ B_n$ in the critical case
| dc.creator | Brofferio, Sara | |
| dc.creator | Buraczewski, Dariusz | |
| dc.creator | Damek, Ewa | |
| dc.date | 2008-09-10 | |
| dc.date | 2008-11-10 | |
| dc.date.accessioned | 2026-07-07T10:16:46Z | |
| dc.date.available | 2026-07-07T10:16:46Z | |
| dc.description | We consider the autoregressive model on $\R^d$ defined by the following stochastic recursion $X_n = A_n X_{n-1}+B_n$, where $\{(B_n,A_n)\}$ are i.i.d. random variables valued in $\R^d\times \R^+$. The critical case, when $\E\big[\log A_1\big]=0$, was studied by Babillot, Bougeorol and Elie, who proved that there exists a unique invariant Radon measure $ν$ for the Markov chain $\{X_n \}$. In the present paper we prove that the weak limit of properly dilated measure $ν$ exists and defines a homogeneous measure on $\R^d\setminus \{0\}$. | |
| dc.identifier | https://arxiv.org/abs/0809.1864 | |
| dc.identifier | http://arxiv.org/abs/0809.1864 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/173620 | |
| dc.subject | Probability | |
| dc.subject | 60J10, 60B15, 60G50 | |
| dc.title | On the invariant measure of the random difference equation $X_n=A_n X_{n-1}+ B_n$ in the critical case | |
| dc.type | text |