Parameter estimation in models generated by SDEs with symmetric alpha-stable noise

Abstract

This article considers vector parameter estimators in statistical models generated by Lévy processes. An improved one-step estimator is presented which can be used for improving any other estimator. Combined numerical methods for optimization problems are proposed. A software has been developed and a correspondent testing and comparison have been presented.

Keywords:

• SDE
• Lévy processes
• parameter estimation
• alpha-stable processes
• numerical optimization

MATHEMATICS SUBJECT CLASSIFICATIONS:

• 60-04
• 60G51
• 65C20
• 62F10

Acknowledgments

This research was partially supported by the Alexander von Humboldt Foundation within the Research Group Linkage Programme Singular diffusions: analytic and stochastic approaches between the University of Potsdam and the Institute of Mathematics of the National Academy of Sciences of Ukraine.

Disclosure statement

No potential conflict of interest was reported by the author(s).