Fractional Fokker–Planck equation for nonlinear stochastic differential equations driven by non-Gaussian Lévy stable noises

Nonlinear Stochastic Differential Equations Driven by Non-Gaussian Levy Stable Noises

The Fokker-Planck equation has been very useful for studying dynamic behavior of stochastic differential equations driven by Gaussian

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

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.

Role of the interpretation of stochastic calculus in systems with cross-correlated Gaussian white noises.

We derive the Fokker-Planck equation for multivariable Langevin equations with cross-correlated Gaussian white noises for an arbitrary interpretation of the stochastic differential equation. We formulate the conditions when the solution of the Fokker-Planck equation does not depend on which stochastic calculus is adopted. Further, we derive an equivalent multivariable Ito stochastic differentia...

Phase transitions driven by Lévy stable noise: exact solutions and stability analysis of nonlinear fractional Fokker-Planck equations

Phase transitions and effects of external noise on many body systems are one of the main topics in physics. In mean field coupled nonlinear dynamical stochastic systems driven by Brownian noise, various types of phase transitions including nonequilibrium ones may appear. A Brownian motion is a special case of Lévy motion and the stochastic process based on the latter is an alternative choice fo...

Existence and Measurability of the Solution of the Stochastic Differential Equations Driven by Fractional Brownian Motion