A new development of studies on stochastic process, statistical distributions and representation theory
Project/Area Number |
25610006
|
Research Category |
Grant-in-Aid for Challenging Exploratory Research
|
Allocation Type | Multi-year Fund |
Research Field |
Algebra
|
Research Institution | Kyushu University |
Principal Investigator |
Wakayama Masato 九州大学, 学内共同利用施設等, 教授 (40201149)
|
Project Period (FY) |
2013-04-01 – 2016-03-31
|
Project Status |
Completed (Fiscal Year 2015)
|
Budget Amount *help |
¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000)
Fiscal Year 2015: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2013: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
|
Keywords | 群作用 / 統計(情報)多様体 / Meixner-Pollaczek過程 / α行列式 / 正規分布モデル / 群行列式 / 対称錘 / 等質空間 / 楕円分布モデル |
Outline of Final Research Achievements |
The first theme of the project was to understand, by employing a suitable group action, the mysterious derivation/determination of geodesics on multivariate normal models given by Erisken in 1987. This was completely achieved by Hiroto Inoue, a PhD course student under my supervision. Actually, he proved that the normal model can be realized as a submanifold of a certain (pre-conjectured) Riemannian symmetric space (cone) by Riemann submersion and the mysterious derivation of geodesic follows from this fact. This result may provide a new understanding for the elliptical models including normal models. The second is expanding the representation theoretic study of α-determinant, which was originally defined in the framework of statistical and probability theory, we explored the group-subgroup determinant theory. Moreover, as the third theme, we obtain the fundamental results of multivariate Meixner-Pollaczek polynomials in the framework of harmonic analysis on Hermite symmetric spaces.
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Report
(4 results)
Research Products
(37 results)