分数正态逆高斯过程
Fractional Normal Inverse Gaussian Process
摘要：
正态逆高斯过程（NIG）是由Barndorff-Nielsen（1997）通过将具有漂移的布朗运动从属于逆高斯过程而引入的。NIG过程的增量是独立的、平稳的。本文通过将分数布朗运动从属于一个逆高斯过程，引入了NIG过程增量之间的依赖关系，称之为分数正态逆高斯过程（FNIG）。讨论了这一过程的基本性质。它的边缘分布是正态分布的尺度混合，对于Hurst参数1/2<=H< 1是无限可分的，并且是重尾的。该过程的一阶增量是平稳的，具有长程相关性。证明了它们也具有符号持久性LRD性质。本文还讨论了一个推广的FNIG过程，称为n-FNIG过程，它允许Hurst参数H在区间（n-1，n）内。可能的应用数学金融和水力学也指出
英文摘要：
Normal inverse Gaussian (NIG) process was introduced by Barndorff-Nielsen (1997) by subordinating Brownian motion with drift to an inverse Gaussian process. Increments of NIG process are independent and 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< 1 and are heavy tailed. First order increments of the process are stationary and possess long-range dependence (LRD) property. It is shown that they have persistence of signs LRD property also. A generalization of the FNIG process called n-FNIG process is also discussed which allows Hurst parameter H in the interval (n-1, n). Possible applications to mathematical finance and hydraulics are also pointed out
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