Equivalence of subordinated processes with tempered \(\alpha\)-stable waiting times and fractional Fokker-Planck equations in space and time dependent fields. (English) Zbl 1327.82071
Summary: 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.
MSC:
82C31 | Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics |
35Q84 | Fokker-Planck equations |
35R11 | Fractional partial differential equations |
26A33 | Fractional derivatives and integrals |
Keywords:
subordinated processes; tempered \(\alpha\)-stable processes; fractional Fokker-Planck equationReferences:
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