  Let $(X_t,t\geq 0)$ be a random walk on $\mathbb{Z}^d$. Let $ l_T(x)=
\int_0^T \delta_x(X_s)ds$ the local time at the state $x$ and $ I_T=
\sum\limits_{x\in\mathbb{Z}^d} l_T(x)^q $ the q-fold self-intersection local
time (SILT). In \cite{Castell} Castell proves a large deviations principle for
the SILT of the simple random walk in the critical case $q(d-2)=d$. In the
supercritical case $q(d-2)>d$, Chen and M\"orters obtain in \cite{ChenMorters}
a large deviations principle for the intersection of $q$ independent random
walks, and Asselah obtains in \cite{Asselah5} a large deviations principle for
the SILT with $q=2$. We extend these results to an $\alpha$-stable process
(i.e. $\alpha\in]0,2]$) in the case where $q(d-\alpha)\geq d$.
