Large deviations for self-intersection local times of stable random walks

Let (Xt,t>=0) be a random walk on . Let be the local time at the state x and the q-fold self-intersection local time (SILT). In [5] 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 Mörters obtain in [10] a large deviations principle for the intersection of q independent random walks, and Asselah obtains in [1] a large deviations principle for the SILT with q=2. We extend these results to an [alpha]-stable process (i.e. [alpha][set membership, variant]]0,2]) in the case where q(d-[alpha])>=d.