Abstract: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".
From: Richard Aoun [view email]
[v1]
Wed, 7 Aug 2024 15:50:32 UTC (28 KB)
[v2]
Fri, 24 Jul 2026 11:22:37 UTC (29 KB)
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