On invariant measures of stochastic recursions in a critical case
| dc.creator | Buraczewski, Dariusz | |
| dc.date | 2007-10-19 | |
| dc.date.accessioned | 2026-07-07T08:38:18Z | |
| dc.date.available | 2026-07-07T08:38:18Z | |
| dc.description | We consider an autoregressive model on $\mathbb{R}$ defined by the recurrence equation $X_n=A_nX_{n-1}+B_n$, where $\{(B_n,A_n)\}$ are i.i.d. random variables valued in $\mathbb{R}\times\mathbb{R}^+$ 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 $\{X_n\}$. 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. | |
| dc.description | Published in at http://dx.doi.org/10.1214/105051607000000140 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org) | |
| dc.identifier | https://arxiv.org/abs/0710.3687 | |
| dc.identifier | http://arxiv.org/abs/0710.3687 | |
| dc.identifier | Annals of Applied Probability 2007, Vol. 17, No. 4, 1245-1272 | |
| dc.identifier | doi:10.1214/105051607000000140 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/140680 | |
| dc.subject | Probability | |
| dc.subject | 60J10 (Primary) 60B15, 60G50 (Secondary) | |
| dc.title | On invariant measures of stochastic recursions in a critical case | |
| dc.type | text |