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Continuous time random walk and parametric subordination in fractional diffusion | | Rudolf Gorenflo
; Francesco Mainardi
; Alessandro Vivoli
; | | Date: |
6 Jan 2007 | | Subject: | Statistical Mechanics | | Abstract: | The well-scaled transition to the diffusion limitin 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. We treat the CTRW as a combination of a random walk on the axis of physical time with a random walk in space, both walks happening in discrete operational time. In the continuum limit we obtain a generally non-Markovian 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. By what we call parametric subordination, applied to a combination of a Markov process with a positively oriented L’evy process, we generate and display sample paths for some special cases. | | Source: | arXiv, cond-mat/0701126 | | Services: | Forum | Review | PDF | Favorites | |
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