Stochastic model for ultraslow diffusion
Ultraslow diffusion is a physical model in which a plume of diffusing particles spreads at a logarithmic rate. Governing partial differential equations for ultraslow diffusion involve fractional time derivatives whose order is distributed over the interval from zero to one. This paper develops the stochastic foundations for ultraslow diffusion based on random walks with a random waiting time between jumps whose probability tail falls off at a logarithmic rate. Scaling limits of these random walks are subordinated random processes whose density functions solve the ultraslow diffusion equation. Along the way, we also show that the density function of any stable subordinator solves an integral equation (5.15) that can be used to efficiently compute this function.
Year of publication: |
2006
|
---|---|
Authors: | Meerschaert, Mark M. ; Scheffler, Hans-Peter |
Published in: |
Stochastic Processes and their Applications. - Elsevier, ISSN 0304-4149. - Vol. 116.2006, 9, p. 1215-1235
|
Publisher: |
Elsevier |
Keywords: | Continuous time random walk Slowly varying tails Anomalous diffusion Stable subordinator |
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