  We consider the following recurrence relation with random i.i.d. coefficients
$(a_n,b_n)$: $$ x_{n+1}=a_{n+1} x_n+b_{n+1} $$ where $a_n\in
GL(d,\mathbb{R}),b_n\in \mathbb{R}^d$. Under natural conditions on $(a_n,b_n)$
this equation has a unique stationary solution, and its support is non-compact.
We show that, in general, its law has a heavy tail behavior and we study the
corresponding directions. This provides a natural construction of laws with
heavy tails in great generality. Our main result extends to the general case
the results previously obtained by H. Kesten in [16] under positivity or
density assumptions, and the results recently developed in [17] in a special
framework.
