Stochastic model for ultraslow diffusion |
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Authors: | Mark M Meerschaert Hans-Peter Scheffler |
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Institution: | 1. Department of Mathematics and Statistics, University of Otago, New Zealand;2. Department of Mathematics, University of Siegen, Germany |
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Abstract: | 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. |
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Keywords: | primary 60G50 60F17 secondary 60H30 82C31 |
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