Fractional normal inverse Gaussian diffusion

A. Kumar, Mark M. Meerschaert and P. Vellaisamy

Statistics & Probability Letters, 2011, vol. 81, issue 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.

Keywords: Continuous; time; random; walk; Fractional; Brownian; motion; Normal; inverse; Gaussian; process; Subordination (search for similar items in EconPapers)
Date: 2011
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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