Scale-invariant Truncated L\'evy Process

TL;DR

This paper introduces a scale-invariant truncated Lévy process that models correlated stochastic systems with finite moments, capturing empirical scaling behaviors observed in data such as finance.

Contribution

It presents a novel STL process combining Lévy stability with finite moments, suitable for modeling physical and financial systems with empirical scaling.

Findings

The STL process exhibits Lévy stability and finite moments.

It effectively models empirical scaling in financial data.

The process can describe correlated stochastic variables in physical systems.

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.