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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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.References
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Additional Information
- Marcin Magdziarz
- Affiliation: Hugo Steinhaus Center, Department of Mathematics, Wroclaw University of Technology, 50-370 Wroclaw, Poland
- Email: marcin.magdziarz@pwr.wroc.pl
- Tomasz Zorawik
- Affiliation: Hugo Steinhaus Center, Department of Mathematics, Wroclaw University of Technology, 50-370 Wroclaw, Poland
- MR Author ID: 1057026
- Received by editor(s): September 3, 2014
- Received by editor(s) in revised form: April 10, 2015
- Published electronically: October 5, 2015
- Communicated by: Mark M. Meerschaert
- © Copyright 2015 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 144 (2016), 1767-1778
- MSC (2010): Primary 60G51; Secondary 60G22
- DOI: https://doi.org/10.1090/proc/12856
- MathSciNet review: 3451252