Quantifying model uncertainty in dynamical systems driven by non-Gaussian Lévy stable noise with observations on mean exit time or escape probability

Abstract

Complex systems are sometimes subject to non-Gaussian α-stable Lévy fluctuations. A new method is devised to estimate the uncertain parameter α and other system parameters, using observations on mean exit time or escape probability for the system evolution. It is based on solving an inverse problem for a deterministic, nonlocal partial differential equation via numerical optimization. The existing methods for estimating parameters require observations on system state sample paths for long time periods or probability densities at large spatial ranges. The method proposed here, instead, requires observations on mean exit time or escape probability only for an arbitrarily small spatial domain. This new method is beneficial to systems for which mean exit time or escape probability is feasible to observe.