| 功率谱流形上的Jacobi场 |
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| 引用本文： | 弗洛斯,段晓敏,孙华飞.功率谱流形上的Jacobi场[J].北京理工大学学报,2013,33(8):862-865. |
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| 作者姓名： | 弗洛斯 段晓敏 孙华飞 |
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| 作者单位： | 北京理工大学 数学学院,北京,100081;北京理工大学 数学学院,北京,100081;北京理工大学 数学学院,北京,100081 |
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| 基金项目： | 国家自然科学基金资助项目(61179031,10932002) |
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| 摘 要： | 从微分几何的角度,将功率谱的集合看成一个微分流形. 引入流形上的黎曼度量及单参数仿射联络族, 介绍了功率谱流形的几何结构, 并且给出若干随机模型的数量曲率.研究了流形上的Jacobi场,进而考虑功率谱流形上测地线的收敛性,并以随机过程模型AR(1)为例说明结果.
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| 关 键 词： | 功率谱 微分几何 Jacobi场 |
| 收稿时间： | 2012/9/18 0:00:00 |
Jacobi Fields on the Manifold of Power Spectral |
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| SYED Feroz-shah,DUAN Xiao-min and SUN Hua-fei.Jacobi Fields on the Manifold of Power Spectral[J].Journal of Beijing Institute of Technology(Natural Science Edition),2013,33(8):862-865. |
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| Authors: | SYED Feroz-shah DUAN Xiao-min and SUN Hua-fei |
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| Institution: | School of Mathematics, Beijing Institute of Technology, Beijing 100081, China |
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| Abstract: | In the view of differential geometry, the set of power spectral is taken as a differential manifold. Moreover, the Riemannian metric and affine dual connections are introduced. Then, the geometric structure of power spectral manifold and its Jacobi fields are investigated. The scalar curvatures of several stochastic process models are given. Further, the instability of the geodesics on manifold is discussed. Finally, the stochastic process model is utilized to illustrate our results. |
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| Keywords: | power spectral differential geometry Jacobi field |
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