Rare-event Modeling for Dynamical Systems and Its Applications: Stable Distribution Approach

Abstract

When we model dynamic phenomena, it is important to properly incorporate their probabilistic uncertainty. In particular, there is an increasing need for modeling and analysis methods for rare events that cause severe impact, e.g., extreme wind power fluctuations due to gusts. For the modeling of the stochasticity in dynamical systems, Gaussian noise is often used because of its analytical tractability. However, it cannot represent outliers because of its rapidly decaying tails. In this context, this article introduces a modeling and analysis method using stable distributions. This framework is capable of modeling rare events while retaining the favorable properties equipped with the Gaussian. As applications, we also describe our results on stochastic linearization analysis and privacy protection in dynamical systems.