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.