Equivalence of Subordinated Processes with Tempered $$\alpha $$ α -Stable Waiting Times and Fractional Fokker–Planck Equations in Space and Time Dependent Fields

Abstract

In this paper we introduce a subordinated stochastic process controlled by tempered \(\alpha \)-stable waiting times and prove the equivalence of this process and the fractional Fokker–Planck equation with space and time dependent diffusion coefficients in the influence of an external space and time dependent force.