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

TL;DR

This paper introduces a stochastic least action principle incorporating heavy-tailed distributions to model rare, impactful black swan events in non-dissipative systems, emphasizing the suitability of Tsallis entropy over Shannon entropy.

Contribution

It formulates a stochastic least action principle using Tsallis entropy to better describe black swan events characterized by heavy tails and non-local correlations.

Findings

Tsallis entropy effectively models black swan events.

Path probability distributions align with non-additive entropy.

Heavy-tailed distributions capture rare event dynamics.

Abstract

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.