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功率谱流形上的Jacobi场

Keywords: 功率谱,微分几何,Jacobi场

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Abstract:

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.

References

[1]  Wolf K B,Krotzsch G. Geometry and dynamics in the fractional discrete Fourier transform[J]. J Opt Soc Am A, 2007,24:651-658.
[2]  Tao R, Deng B, Zhang W, et al. Sampling and sampling rate conversionof band limited signals in the fractional Fourier transform domain[J]. IEEE Transactions on Signal Processing, 2008,56:158-171.
[3]  Amari S. Differential geometrical methods in statistics[M]. Berlin: Springer-Verlag, 1985.
[4]  Amari S, Nagaoka H. Methods of information geometry[M]. Oxford: Oxford University Press, 2000.
[5]  Cafaro C, Ali S A. Jacobi fields on statistical manifolds of negative curvature[J]. Physica D, 2007,234(1):70-80.
[6]  Casetti L, Pettini M, Cohen E G D. Geometric approach to Hamiltonian dynamics and statistical mechanics[J]. Physics Reports, 2000,337(3):237-341.
[7]  Duan X M, Sun H F. Jacobi fields on the manifold of nonsingular hermitematrices[J]. Journal of Beijing Institute of Technology, 2011,31(11):1375-1378.(in Chinese)
[8]  Tanaka F, Komaki F. The sectional curvatures of AR model manifolds[J]. Tensor N S, 2003,64:131-143.
[9]  Tanaka F, Komaki F. Asymptotic expansion of the risk difference of the Bayesianspectral density in the ARMA model[J]. METR, 2005,2005:1-31.
[10]  Kumon M,Amari S. Geometrical theory of higher-order asymptotic of test[J]. Interval Estimator and Conditional Inference, Proc Roy Soc London Set. A, 1983,387:429-458.
[11]  弗洛斯,彭林玉,孙华飞,等.功率谱的信息几何[J].北京理工大学学报,2013,33(3):327-330. Syed Ferozshah, Peng Linyu, Sun Huafei, et al. Information geomtry of power spectra[J]. Transactions of Beijing Institure of Technology, 2013,33(3):327-330. (in Chinese)

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