IRIS Università degli Studi di Bolognahttps://cris.unibo.itIl sistema di repository digitale IRIS acquisisce, archivia, indicizza, conserva e rende accessibili prodotti digitali della ricerca.Sat, 05 Dec 2020 15:09:23 GMT2020-12-05T15:09:23Z1041Discrete and continuous random walk models
for space-time fractional diffusionhttp://hdl.handle.net/11585/17784Titolo: Discrete and continuous random walk models
for space-time fractional diffusion
Abstract: A mathematical approach to anomalous diffusion
may be based on generalized diffusion equations
(containing derivatives of fractional
order in space or/and time)
and related random walk models.
A more general approach is however provided by the integral equation for the so-called continuous time random walk (CTRW), which can be understood as a random walk
subordinated to a renewal process.
We show how this integral equation reduces
to our fractional diffusion equations by a properly scaled
passage to the limit of compressed waiting times and jumps.
The essential assumption is that the probabilities for
waiting times and jumps behave asymptotically
like powers with negative exponents related to the
orders of the fractional derivatives.
Illustrating examples are given, numerical results and plots of
simulations are displayed.
Thu, 01 Jan 2004 00:00:00 GMThttp://hdl.handle.net/11585/177842004-01-01T00:00:00ZRenewal processes of Mittag-Leffler and Wright typehttp://hdl.handle.net/11585/17558Titolo: Renewal processes of Mittag-Leffler and Wright type
Abstract: After sketching the basic principles of renewal theory we discuss the classical Poisson process and offer two other processes,
namely the renewal process of Mittag-Leffler type and the
renewal process of Wright type, so named by us because special functions of Mittag-Leffler and of Wright type appear in the definition of the relevant waiting times. We compare these three processes with each other, furthermore consider corresponding renewal processes with reward and numerically their long-time behaviour.
Sat, 01 Jan 2005 00:00:00 GMThttp://hdl.handle.net/11585/175582005-01-01T00:00:00ZSubordination in fractional diffusion via continuous time random walkhttp://hdl.handle.net/11585/80814Titolo: Subordination in fractional diffusion via continuous time random walk
Abstract: The well-scaled transition to the diffusion limit in the framework of the theory of continuous-time random walk (CTRW) is presented starting from its representation as an infinite series that points out the subordinated character of the CTRW itself. This formula allows us to treat the CTRW as a discrete-space discrete-time random walk that in the continuum limit tends towards a generalized diffusion process governed by a space-time fractional diffusion equation. The essential assumption is that the probabilities for
waiting times and jump-widths behave asymptotically like powers with negative exponents related to the orders of the fractional
derivatives. Plots of simulations for some case-studies are given
in order to display the sample paths for the fractional
diffusion processes, generally non Markovian, that are obtained
by the composition of two Markovian processes.
Thu, 01 Jan 2009 00:00:00 GMThttp://hdl.handle.net/11585/808142009-01-01T00:00:00ZContinuous time random walk and time fractional diffusion:
a numerical comparison between the fundamental solutionshttp://hdl.handle.net/11585/17593Titolo: Continuous time random walk and time fractional diffusion:
a numerical comparison between the fundamental solutions
Abstract: We consider the basic models for anomalous transport provided
by the integral equation for continuous time random walk (CTRW)
and by the time fractional diffusion equation to which the previous
equation is known to reduce in the diffusion limit.
We compare the corresponding fundamental solutions of these
equations, in order to investigate numerically the increasing
quality of approximation with advancing time.
Sat, 01 Jan 2005 00:00:00 GMThttp://hdl.handle.net/11585/175932005-01-01T00:00:00Z