Heavy tail properties of stationary solutions of multidimensional stochastic recursions
| dc.creator | Guivarc'h, Yves | |
| dc.date | 2006-08-10 | |
| dc.date.accessioned | 2026-07-07T07:21:36Z | |
| dc.date.available | 2026-07-07T07:21:36Z | |
| dc.description | We consider the following recurrence relation with random i.i.d. coefficients $(a_n,b_n)$: $$ x_{n+1}=a_{n+1} x_n+b_{n+1} $$ where $a_n\in GL(d,\mathbb{R}),b_n\in \mathbb{R}^d$. Under natural conditions on $(a_n,b_n)$ this equation has a unique stationary solution, and its support is non-compact. We show that, in general, its law has a heavy tail behavior and we study the corresponding directions. This provides a natural construction of laws with heavy tails in great generality. Our main result extends to the general case the results previously obtained by H. Kesten in [16] under positivity or density assumptions, and the results recently developed in [17] in a special framework. | |
| dc.description | Published at http://dx.doi.org/10.1214/074921706000000121 in the IMS Lecture Notes--Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org) | |
| dc.identifier | https://arxiv.org/abs/math/0608239 | |
| dc.identifier | http://arxiv.org/abs/math/0608239 | |
| dc.identifier | IMS Lecture Notes--Monograph Series 2006, Vol. 48, 85-99 | |
| dc.identifier | doi:10.1214/074921706000000121 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/115355 | |
| dc.subject | Probability | |
| dc.subject | 60G50, 60H25 (Primary) 37B05 (Secondary) | |
| dc.title | Heavy tail properties of stationary solutions of multidimensional stochastic recursions | |
| dc.type | text |