A stochastic least action principle applied in the description of black swan events

In this paper we present a formulation of the stochastic least action principle (SAP) to encompass random movements with black swan events (of non dissipative systems) in terms of heavy tailed distributions. The black swan events are rare and drastic events, such as earthquakes and financial crisis. It has been observed that the Tsallis entropy suits well in the description of the black swan events rather than the Shannon-Boltzman-Gibbs entropy, which is intrinsically related to the fact that black swan events of physical systems are proportional to non-local correlations. As a consequence, we could assess the validity of the path probability distribution obtained using the non-additive Tsallis entropy.