  Complex systems are sometimes subject to non Gaussian alpha stable Levy
fluctuations. A new method is devised to estimate this uncertain parameter and
other system parameters, using observations on either mean exit time or escape
probability for the system evolution. It is based on solving an inverse problem
for a deterministic, non-local 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.
