Jacobi Fields on the Manifold of Power Spectral

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.