Truncated Levy process with scale-invariant behavior

We develop a scale-invariant truncated Levy (STL) process to describe physi cal systems characterized by correlated stochastic variables. The STL proce ss exhibits Levy stability for the probability density, and hence shows sca ling properties (as observed in empirical data); it has the advantage that all moments are finite (and so accounts for the empirical scaling of the mo ments). To test the potential utility of the STL process, we analyze financ ial data. (C) 2001 Elsevier Science B.V. All rights reserved.