  We consider the autoregressive model on $\R^d$ defined by the following
stochastic recursion $X_n = A_n X_{n-1}+B_n$, where $\{(B_n,A_n)\}$ are i.i.d.
random variables valued in $\R^d\times \R^+$. The critical case, when
$\E\big[\log A_1\big]=0$, was studied by Babillot, Bougeorol and Elie, who
proved that there exists a unique invariant Radon measure $\nu$ for the Markov
chain $\{X_n \}$. In the present paper we prove that the weak limit of properly
dilated measure $\nu$ exists and defines a homogeneous measure on
$\R^d\setminus \{0\}$.
