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|Title: ||Fractional normal inverse Gaussian diffusion|
|Authors: ||KUMAR, A|
|Keywords: ||TIME RANDOM-WALKS|
|Issue Date: ||2011|
|Publisher: ||ELSEVIER SCIENCE BV|
|Citation: ||STATISTICS & PROBABILITY LETTERS,81(1)146-152|
|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. (C) 2010 Elsevier B.V. All rights reserved.|
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