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arXiv · 0911.1176

On q-Gaussians and Exchangeability

Marjorie G. Hahn·Xinxin Jiang·Sabir Umarov
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Abstract

The q-Gaussians are discussed from the point of view of variance mixtures of normals and exchangeability. For each q< 3, there is a q-Gaussian distribution that maximizes the Tsallis entropy under suitable constraints. This paper shows that q-Gaussian random variables can be represented as variance mixtures of normals. These variance mixtures of normals are the attractors in central limit theorems for sequences of exchangeable random variables; thereby, providing a possible model that has been extensively studied in probability theory. The formulation provided has the additional advantage of yielding process versions which are naturally q-Brownian motions. Explicit mixing distributions for q-Gaussians should facilitate applications to areas such as option pricing. The model might provide insight into the study of superstatistics.

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Marjorie G. Hahn, Xinxin Jiang, Sabir Umarov. 2009-11-06. On q-Gaussians and Exchangeability. https://doi.org/10.1088/1751-8113%2F43%2F16%2F165208

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