I am pricing an American call under the CGMY model ($0 < Y < 1$) with strike $K$ at grid point $(x_i,\tau_j)$ where $x_i=x_{min}+i\,\Delta x $ for $i=0,1,...N$ and $\Delta x=\frac{x_{max}-x_{min}}{N}$.Why in the region $y\in(x_N-x_i,\infty)$ we have
\begin{align} \int_{x_N-x_i}^{\infty}(w(x_i+y,\tau_j)-w(x_i,\tau_j))\frac{exp(-\lambda_p) y}{\nu(x_i,\tau_j)\, y^{1+Y}}\,\,dy=0 \end{align}
Where $w(x_i,\tau_j)$ is the premium at $(x_i,\tau_j)$.