We consider the products Gₙ = Aₙ A₁ of independent and identical distributed nonnegative d d matrices (Aᵢ) ₈ ₁. For any starting point x R_+ᵈ with unit norm, we establish the convergence to a stable law for the norm cocycle | Gₙx |, jointly with its direction Gₙ x = Gₙ x / | Gₙ x |. We also prove a local limit theorem for the couple (|Gₙx|, Gₙ x), and find the exact rate of its convergence.
Mei et al. (Mon,) studied this question.