Stochastic representation of a fractional subdiffusion equation. The case of infinitely divisible waiting times, Lévy noise and space-time-dependent coefficients

Magdziarz, Marcin; Zorawik, Tomasz

doi:10.1090/proc/12856

Stochastic representation of a fractional subdiffusion equation. The case of infinitely divisible waiting times, Lévy noise and space-time-dependent coefficients
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Proc. Amer. Math. Soc. 144 (2016), 1767-1778 Request permission

Abstract:

In this paper we analyze a fractional Fokker-Planck equation describing subdiffusion in the general infinitely divisible (ID) setting. We show that in the case of space-time-dependent drift and diffusion and time-dependent jump coefficients, the corresponding stochastic process can be obtained by subordinating a two-dimensional system of Langevin equations driven by appropriate Brownian and Lévy noises. Our result solves the problem of stochastic representation of subdiffusive Fokker-Planck dynamics in full generality.

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