  The aim of the present paper is to extend the large deviation with
discontinuous statistics studied in \cite{BDE} to the diffusion
$d\mathbf{x}^\varepsilon = -\{\mathbf{A}^\top (\mathbf{A}
\mathbf{x}^\varepsilon - \mathbf{y}) + \mu sgn(\mathbf{x}^\varepsilon)\}dt +
\varepsilon d\mathbf{w}$. The discontinuity of the drift of the diffusion
discussed in \cite{BDE} is equal to the hyperplane $\{\mathbf{x} \in
\mathbb{R}^d:\ x_1=0\}$, however, in our case the discontinuity is more complex
and is equal to the set $\{\mathbf{x} \in \mathbb{R}^d:\ \prod_{i=1}^dx_i=0\}$.
