Scale-invariant Truncated L\'evy Process

Abstract

We develop a scale-invariant truncated L\'evy (STL) process to describe physical systems characterized by correlated stochastic variables. The STL process exhibits L\'evy 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.