Power-law behaviors from the two-variable Langevin equation: Ito's and Stratonovich's Fokker-Planck equations

Abstract

We study power-law behaviors produced from the stochastically dynamical system governed by the well-known two-variable Langevin equations. The stationary solutions of the corresponding Ito's, Stratonovich's and the Zwanzig's (the backward Ito's) Fokker-Planck equations are solved under a new fluctuation-dissipation relation, which are presented in a unified form of the power-law distributions with a power index containing two parameter kappa and sigma, where kappa measures a distance away from the thermal equilibrium and sigma distinguishes the above three forms of the Fokker-Planck equations. The numerical calculations show that the Ito's, the Stratonovich's and the Zwanzig's form of the power-law distributions are all exactly the stationary solutions based on the two-variable Langevin equations.

12 pages,6 figures, 41 references

References in corpus (5)

• Superdiffusion and non-Gaussian statistics in a driven-dissipative 2D dusty plasma
• Relativistic Brownian Motion
• Power-Law Distributions for a Trapped Ion Interacting with a Classical Buffer Gas
• Thermostatistics of overdamped motion of interacting particles
• Acoustic Kappa-Density Fluctuation Waves in Suprathermal Kappa Function Fluids

Cited by in corpus (4)

• Transport coefficients in Lorentz plasmas with the power-law kappa-distribution
• The nonextensive parameter for nonequilibrium plasmas in magnetic field
• The nonextensive statistical ensembles with dual thermodynamic interpretations
• The collisional relaxation rate of kappa-distributed plasma with multiple components