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Discrete random walk models for symmetric Levy-Feller diffusion processes
We propose a variety of models of random walk, discrete in space and time,
suitable for simulating stable random variables of arbitrary index
(), in the symmetric case. We show that by properly scaled
transition to vanishing space and time steps our random walk models converge to
the corresponding continuous Markovian stochastic processes, that we refer to
as Levy-Feller diffusion processes.Comment: 13 pages, 3 figures, to be published in Physica
Subordination Pathways to Fractional Diffusion
The uncoupled Continuous Time Random Walk (CTRW) in one space-dimension and
under power law regime is splitted into three distinct random walks: (rw_1), a
random walk along the line of natural time, happening in operational time;
(rw_2), a random walk along the line of space, happening in operational
time;(rw_3), the inversion of (rw_1), namely a random walk along the line of
operational time, happening in natural time. Via the general integral equation
of CTRW and appropriate rescaling, the transition to the diffusion limit is
carried out for each of these three random walks. Combining the limits of
(rw_1) and (rw_2) we get the method of parametric subordination for generating
particle paths, whereas combination of (rw_2) and (rw_3) yields the
subordination integral for the sojourn probability density in space-time
fractional diffusion.Comment: 20 pages, 4 figure
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