Fractional- and integer-order moments, and multiscaling for smoothly truncated Lévy flights

We study multiscale properties of smoothly truncated Lévy flights. The behavior of both fractional- and integer-order moments 〈ρ|Xa(t)|〉〈|Xa(t)|ρ〉, for both small and large values of the scaling parameter a is investigated. In the former case we obtain the behavior close to that of the α-stable flight, and for the latter, close to that of the Brownian motion.