Scale-invariant truncated Levy process

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 distribution, and hence shows scaling pr operties as commonly observed in empirical data; it has the advantage that all moments are finite and so accounts for the empirical scaling of the mom ents. To test the potential utility of the STL process, we analyze financia l data.