Abstract
A φ-exponential distribution is a generalization of an exponential distribution associated to functions φ in an appropriate class, and the space of φ-exponential distributions has a dually flat structure. We study features of the space of φ-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.
| Original language | English |
|---|---|
| Pages (from-to) | 2546-2556 |
| Number of pages | 11 |
| Journal | SIAM Journal on Mathematical Analysis |
| Volume | 45 |
| Issue number | 4 |
| DOIs | |
| Publication status | Published - 2013 |
| Externally published | Yes |
Keywords
- Evolution equation
- Q-Gaussian measure
- Wasserstein geometry
- φ-Exponential distribution
ASJC Scopus subject areas
- Analysis
- Computational Mathematics
- Applied Mathematics