BEHAVIORS OF φ-EXPONENTIAL DISTRIBUTIONS IN WASSERSTEIN GEOMETRY AND AN EVOLUTION EQUATION

被引：3
|
作者：
Takatsu, Asuka [1 ,2 ]
机构：
[1] Nagoya Univ, Grad Sch Math, Nagoya, Aichi 4648602, Japan
[2] Inst Hautes Etud Sci, F-91440 Bures Sur Yvette, France
来源：
SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 2013年 / 45卷 / 04期
关键词：
phi-exponential distribution; q-Gaussian measure; Wasserstein geometry; evolution equation;
D O I：
10.1137/110849304
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A phi-exponential distribution is a generalization of an exponential distribution associated to functions phi in an appropriate class, and the space of phi-exponential distributions has a dually flat structure. We study features of the space of phi-exponential distributions, such as the convexity in Wasserstein geometry and the stability under an evolution equation. From this study, we provide the new characterizations to the space of Gaussian measures and the space of q-Gaussian measures.
引用
收藏
页码：2546 / 2556
页数：11
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