Fractional Normal Inverse Gaussian Process

Arun Kumar and Palaniappan Vellaisamy ()
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Arun Kumar: Indian Institute of Technology Bombay
Palaniappan Vellaisamy: Indian Institute of Technology Bombay

Methodology and Computing in Applied Probability, 2012, vol. 14, issue 2, 263-283

Abstract: Abstract Normal inverse Gaussian (NIG) process was introduced by Barndorff-Nielsen (Scand J Statist 24:1–13, 1997) by subordinating Brownian motion with drift to an inverse Gaussian process. Increments of NIG process are independent and are stationary. In this paper, we introduce dependence between the increments of NIG process, by subordinating fractional Brownian motion to an inverse Gaussian process and call it fractional normal inverse Gaussian (FNIG) process. The basic properties of this process are discussed. Its marginal distributions are scale mixtures of normal laws, infinitely divisible for the Hurst parameter 1/2 ≤ H

Keywords: Fractional Brownian motion; Fractional normal inverse Gaussian process; Generalized gamma convolutions; Infinite divisibility; Long-range dependence; Subordination; Primary 60G22; Secondary 60G07, 60G15 (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/s11009-010-9201-z

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