Bounds for the expected number of level crossings of certain harmonizable infinitely divisible processes

Let ENu(0,1) denote the expected number of crossings of a level u, in a fixed time interval [0,1], by a large class of real valued symmetric stationary harmonizable infinitely divisible processes which includes stationary harmonizable stable processes. Equivalent upper and lower bounds are given for EN0(0,1) and a precise asymptotic limit is given for ENu(0,1), as u → ∞.