Modeling of nonlinear Lévy processes by data analysis

Abstract

The paper presents a method to analyze time series of nonlinear Lévy processes. The Lévy stability index as well as the nonlinear deterministic and stochastic parts of the dynamics together with their uncertainties can be calculated numerically. As last step of the analysis the membership of the investigated system to the regarded class of dynamical systems is validated. For demonstration the algorithm is applied to artificially created time series with different Lévy indices.