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arXiv · 1206.6658

On Some Asymptotic Properties and an Almost Sure Approximation of the Normalized Inverse-Gaussian Process

Luai Al Labadi·Mahmoud Zarepour
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Abstract

In this paper, we present some asymptotic properties of the normalized inverse-Gaussian process. In particular, when the concentration parameter is large, we establish an analogue of the empirical functional central limit theorem, the strong law of large numbers and the Glivenko-Cantelli theorem for the normalized inverse-Gaussian process and its corresponding quantile process. We also derive a finite sum-representation that converges almost surely to the Ferguson and Klass representation of the normalized inverse-Gaussian process. This almost sure approximation can be used to simulate efficiently the normalized inverse-Gaussian process.

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Luai Al Labadi, Mahmoud Zarepour. 2012-06-28. On Some Asymptotic Properties and an Almost Sure Approximation of the Normalized Inverse-Gaussian Process. https://arxiv.org/abs/1206.6658

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