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

摘要

We derive analytic solutions for the full time dependence of space-fractional Fokker-Planck equations corresponding to stochastic Langevin equations with additive tempered-stable Levy 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.