Weakly dependent chains with infinite memory
| dc.creator | Doukhan, Paul | |
| dc.creator | Wintenberger, Olivier | |
| dc.date | 2007-12-19 | |
| dc.date.accessioned | 2026-07-07T08:50:23Z | |
| dc.date.available | 2026-07-07T08:50:23Z | |
| dc.description | We prove the existence of a weakly dependent strictly stationary solution of the equation $ X_t=F(X_{t-1},X_{t-2},X_{t-3},...;ξ_t)$ called {\em chain with infinite memory}. Here the {\em innovations} $ξ_t$ constitute an independent and identically distributed sequence of random variables. The function $F$ takes values in some Banach space and satisfies a Lipschitz-type condition. We also study the interplay between the existence of moments and the rate of decay of the Lipschitz coefficients of the function $F$. With the help of the weak dependence properties, we derive Strong Laws of Large Number, a Central Limit Theorem and a Strong Invariance Principle. | |
| dc.description | Stochastic Processes and their Applications (2008) accepté | |
| dc.identifier | https://arxiv.org/abs/0712.3231 | |
| dc.identifier | http://arxiv.org/abs/0712.3231 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/144588 | |
| dc.subject | Probability | |
| dc.subject | Statistics Theory | |
| dc.title | Weakly dependent chains with infinite memory | |
| dc.type | text |