  A theoretical approach for characterising the influence of asymmetry of noise
distribution on the escape rate of a multi-stable system is presented. This was
carried out via the estimation of an action, which is defined as an exponential
factor in the escape rate, and discussed in the context of full counting
statistics paradigm. The approach takes into account all cumulants of the noise
distribution and demonstrates an excellent agreement with the results of
numerical simulations. An approximation of the third order cumulant was shown
to have limitations on the range of dynamic stochastic system parameters. The
applicability of the theoretical approaches developed so far is discussed for
an adequate characterisation of the escape rate measured in experiments.
