2021/09/30 by Yang Li, Li, Yang, Yubin Lu +5 · 2 citations
Economics, Econometrics and Finance · Environmental Science · #Data Analysis #FOS: Computer and information sciences #FOS: Mathematics #FOS: Physical sciences #Financial Risk and Volatility Modeling #Hydrology and Drought Analysis #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Probability (math.PR) #Statistics and Probability (physics.data-an) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2109.14881
openalex publication_date 2021/09/30 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28
With the rapid increase of valuable observational, experimental and simulated data for complex systems, much efforts have been devoted to identifying governing laws underlying the evolution of these systems. Despite the wide applications of non-Gaussian fluctuations in numerous physical phenomena, the data-driven approaches to extract stochastic dynamical systems with (non-Gaussian) Lévy noise are relatively few so far. In this work, we propose a data-driven method to extract stochastic dynamical systems with α-stable Lévy noise from short burst data based on the properties of α-stable distributions. More specifically, we first estimate the Lévy jump measure and noise intensity via computing mean and variance of the amplitude of the increment of the sample paths. Then we approximate the drift coefficient by combining nonlocal Kramers-Moyal formulas with normalizing flows. Numerical experiments on one- and two-dimensional prototypical examples illustrate the accuracy and effectiveness of our method. This approach will become an effective scientific tool in discovering stochastic governing laws of complex phenomena and understanding dynamical behaviors under non-Gaussian fluctuations.