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Please use this identifier to cite or link to this item: http://dspace.library.iitb.ac.in/jspui/handle/100/14189

Title: Fractional normal inverse Gaussian diffusion
Authors: KUMAR, A
MEERSCHAERT, MM
VELLAISAMY, P
Keywords: TIME RANDOM-WALKS
LIMIT-THEOREMS
TRANSPORT
DYNAMICS
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.
URI: http://dx.doi.org/10.1016/j.spl.2010.10.007
http://dspace.library.iitb.ac.in/jspui/handle/100/14189
ISSN: 0167-7152
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