Large Deviations of Local Times of Levy Processes

For X(t) a real-valued symmetric Levy process, its characteristic function is E(e I (lambda) X(t))=exp(-t(psi) ((lambda))). Assume that (psi) is regularly varying at infinity with index 1<(beta) <= 2. Let L x t denote the local time of X(t) and L* t =sup x(element of) R L x t . Estimates are obtained for P(L 0 t => y) and P(L* t => y) as y(longrightarrow)(infinity) and t fixed.