Parameters of the fractional Fokker-Planck equation
S. I. Denisov (1, 2), Peter H\"anggi (3), Holger Kantz (1) ((1)Max, Planck Institute for the Physics of Complex Systems, Germany, (2)Sumy State, University, Ukraine, (3)Augsburg University, Germany)
TL;DR
This paper explores how the parameters of the fractional Fokker-Planck equation relate to the noise process in systems driven by heavy-tailed noise, providing explicit formulas for different variance cases.
Contribution
It derives explicit expressions linking fractional Fokker-Planck parameters to the transition density of heavy-tailed noise processes, covering finite and infinite variance scenarios.
Findings
Explicit parameter formulas for finite variance cases
Explicit parameter formulas for infinite variance cases
Enhanced understanding of noise influence on fractional Fokker-Planck dynamics
Abstract
We study the connection between the parameters of the fractional Fokker-Planck equation, which is associated with the overdamped Langevin equation driven by noise with heavy-tailed increments, and the transition probability density of the noise generating process. Explicit expressions for these parameters are derived both for finite and infinite variance of the rescaled transition probability density.
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