Given a sequence (Mn,Qn)n≥1 of i.i.d.\ random variables with
generic copy (M,Q)∈GL(d,R)×Rd, we consider the random
difference equation (RDE) Rn=MnRn−1+Qn,n≥1, and assume
the existence of κ>0 such that \lim_{n \to \infty}(\E{\norm{M_1 ...
M_n}^\kappa})^{\frac{1}{n}} = 1 . We prove, under suitable assumptions, that
the sequence Sn=R1+...+Rn, appropriately normalized, converges in
law to a multidimensional stable distribution with index κ. As a
by-product, we show that the unique stationary solution R of the RDE is
regularly varying with index κ, and give a precise description of its
tail measure. This extends the prior work http://arxiv.org/abs/1009.1728v3 .Comment: 15 page