Fractional normal inverse Gaussian diffusion |
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Authors: | A. KumarMark M. Meerschaert P. Vellaisamy |
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Affiliation: | a Department of Mathematics, Indian Institute of Technology Bombay, Mumbai-400076, Indiab Department of Statistics and Probability, Michigan State University, East Lansing, MI 48824, USA |
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Abstract: | A fractional normal inverse Gaussian (FNIG) process is a fractional Brownian motion subordinated to an inverse Gaussian process. This paper shows how the FNIG process emerges naturally as the limit of a random walk with correlated jumps separated by i.i.d. waiting times. Similarly, we show that the NIG process, a Brownian motion subordinated to an inverse Gaussian process, is the limit of a random walk with uncorrelated jumps separated by i.i.d. waiting times. The FNIG process is also derived as the limit of a fractional ARIMA processes. Finally, the NIG densities are shown to solve the relativistic diffusion equation from statistical physics. |
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Keywords: | Continuous time random walk Fractional Brownian motion Normal inverse Gaussian process Subordination |
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