Truncated Lévy process with scale-invariant behavior

We develop a scale-invariant truncated Lévy (STL) process to describe physical systems characterized by correlated stochastic variables. The STL process exhibits Lévy stability for the probability density, and hence shows scaling properties (as observed in empirical data); it has the advantage that all moments are finite (and so accounts for the empirical scaling of the moments). To test the potential utility of the STL process, we analyze financial data.