功率谱流形上的Jacobi场

Jacobi Fields on the Manifold of Power Spectral

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.

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.