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Complex systems are sometimes subject to non Gaussian alpha stable Levyfluctuations. A new method is devised to estimate this uncertain parameter andother system parameters, using observations on either mean exit time or escapeprobability for the system evolution. It is based on solving an inverse problemfor a deterministic, non-local partial differential equation via numericaloptimization. The existing methods for estimating parameters requireobservations on system state sample paths for long time periods or probabilitydensities at large spatial ranges. The method proposed here, instead, requiresobservations on mean exit time or escape probability only for an arbitrarilysmall spatial domain. This new method is beneficial to systems for which meanexit time or escape probability is feasible to observe.

Quantifying model uncertainty in non-Gaussian dynamical systems with observations on mean exit time or escape probability