Recurrence of multidimensional affine recursions in the critical case
We prove, under different natural hypotheses, that the random multidimensional affine recursion $X_n=A_nX_{n-1}+B_n\in\mathbb{R}^d, n \geq 1,$ is recurrent in the critical case. In particular we cover the cases where the matrices $A_n$ are similarities, invertible, rank 1 or with non negative coeffi...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Journal Article |
| Language: | English |
| Published: |
07-08-2024
|
| Subjects: | |
| Online Access: | Get full text |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | We prove, under different natural hypotheses, that the random
multidimensional affine recursion $X_n=A_nX_{n-1}+B_n\in\mathbb{R}^d, n \geq
1,$ is recurrent in the critical case. In particular we cover the cases where
the matrices $A_n$ are similarities, invertible, rank 1 or with non negative
coefficients.
These results are a consequence of a criterion of recurrence for a large
class of affine recursions on $\mathbb R^d$, based on some moment assumptions
of the so-called ``reverse norm control random variable". |
|---|---|
| DOI: | 10.48550/arxiv.2408.03853 |