  Mathematical models for complex systems under random fluctuations often
certain uncertain parameters. However, quantifying model uncertainty for a
stochastic differential equation with an $\alpha$-stable L\'evy process is
still lacking. Here, we propose an approach to infer all the uncertain
non-Gaussian parameters and other system parameters by minimizing the Hellinger
distance over the parameter space. The Hellinger distance measures the
similarity between an empirical probability density of non-Gaussian
observations and a solution (as a probability density) of the associated
nonlocal Fokker-Planck equation. Numerical experiments verify that our method
is feasible for estimating single and multiple parameters. Meanwhile, we find
an optimal estimation interval of the estimated parameters. This method is
beneficial for extracting governing dynamical system models under non-Gaussian
fluctuations, as in the study of abrupt climate changes in the
Dansgaard-Oeschger events.
