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

2013/11/06 by H. Kleinert, Václav Zatloukal, V. Zatloukal
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Financial Risk and Volatility Modeling #Fractional Differential Equations Solutions #Statistical Mechanics and Entropy #cond-mat.stat-mech #math-ph #math.MP #msc:35R11

paper · pdf · doi:10.1103/physreve.88.052106

published as Phys. Rev. E 88, 052106 (2013) · arXiv admin note: text overlap with arXiv:1210.2630

openalex publication_date 2013/11/06 · arxiv created 2015/03/05 · arxiv updated 2015/03/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Fractional diffusion and Lévy stable processes
• Mathematical Formulation of the Quantum Theory of Electromagnetic Interaction
• Systems with correlations in the variance: Generating power law tails in probability distributions
• Quantum Mechanics of H‐Atom from Path Integrals
• From continuous time random walks to the fractional Fokker-Planck equation
• The Pricing of Options and Corporate Liabilities
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