Recurrence of multidimensional affine recursions in the critical case

Richard Aoun, Sara Brofferio, Marc Peigné

We prove, under different natural hypotheses, that the random multidimensional affine recursion $X_n=A_n{X}_{n-1}+B_n\in {\mathbb{R}}^d,n\ge 1$, is recurrent in the critical case. In…