Analytic solution to space-fractional Fokker-Planck equations for tempered-stable Lévy distributions with spatially linear, time-dependent drift

Abstract

We derive analytic solutions for the full time dependence of space-fractional Fokker-Planck equations corresponding to stochastic Langevin equations with additive tempered-stable Lévy noise terms. The drift terms are generalised to be spatially linear, but may contain arbitrary time dependence such that no steady-state solution is available, even for the deterministic system.

14 pages, 3 figures, preprint accepted by Journal of Physics A

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Cited by in corpus (2)

• Green's functions and the Cauchy problem of the Burgers hierarchy and forced Burgers equation
• Two network Kuramoto-Sakaguchi model under tempered stable Lévy noise