Green function of the double fractional Fokker-Planck equation: Path integral and stochastic differential equations

TL;DR

This paper derives Green functions and solutions for stochastic differential equations related to the double fractional Fokker-Planck equation, providing insights into non-Gaussian heavy-tailed distributions and rare event statistics.

Contribution

It introduces a comprehensive analysis of the double fractional Fokker-Planck equation using path integrals and stochastic differential equations, advancing understanding of heavy-tailed distributions.

Findings

Derived Green functions for the double fractional Fokker-Planck equation

Solved related stochastic differential equations

Discussed path integral framework for non-Gaussian processes

Abstract

The statistics of rare events, the so-called black-swan events, is governed by non-Gaussian distributions with heavy power-like tails. We calculate the Green functions of the associated Fokker-Planck equations and solve the related stochastic differential equations. We also discuss the subject in the framework of path integration.