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


Authors: Marcin Magdziarz and Tomasz Zorawik
Journal: Proc. Amer. Math. Soc. 144 (2016), 1767-1778
MSC (2010): Primary 60G51; Secondary 60G22
DOI: https://doi.org/10.1090/proc/12856
Published electronically: October 5, 2015
MathSciNet review: 3451252
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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.


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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

DOI: https://doi.org/10.1090/proc/12856
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
Article copyright: © Copyright 2015 American Mathematical Society

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