Exponential moments of self-intersection local times of stable random walks in subcritical dimensions

Fabienne Castell, Clément Laurent, Clothilde Mélot

Let $(X_t,t\ge 0)$ be an $\alpha$-stable random walk with values in ${\mathbb{Z}}^d$. Let $l_t(x)={\int }_0^t{\delta }_x(X_s)ds$ be its local time. For $p>1$, not necessarily integer, $I_t = \sum_x l…