Analytic solution to space-fractional Fokker-Planck equations for tempered-stable L\'evy 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 L\'evy 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.
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