Stationary Processes and Linear Systems

Lecture Notes in Control and Information Science - Harmonic Analysis and Rational Approximation ◽

10.1007/11601609_10 ◽

2006 ◽

pp. 159-179

Author(s):

Manfred Deistler

Keyword(s):

Linear Systems ◽

Stationary Processes

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Representation of Strongly Stationary Stochastic Processes

Journal of Applied Mechanics ◽

10.1115/1.2900859 ◽

1993 ◽

Vol 60 (3) ◽

pp. 689-694 ◽

Cited By ~ 1

Author(s):

M. Di Paola

Keyword(s):

Stochastic Process ◽

Stochastic Processes ◽

Linear Systems ◽

Stationary Processes ◽

Orthogonality Conditions ◽

Probabilistic Characterization ◽

Stationary Stochastic Processes ◽

Fixed Order ◽

Strongly Stationary

A generalization of the orthogonality conditions for a stochastic process to represent strongly stationary processes up to a fixed order is presented. The particular case of non-normal delta correlated processes, and the probabilistic characterization of linear systems subjected to strongly stationary stochastic processes are also discussed.

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Statistical applications for equivariant matrices

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/s016117120100446x ◽

2001 ◽

Vol 25 (1) ◽

pp. 53-61

Author(s):

S. H. Alkarni

Keyword(s):

Linear Systems ◽

Fourier Transforms ◽

Toeplitz Matrices ◽

Computational Cost ◽

Special Kind ◽

Circulant Matrices ◽

Stationary Processes ◽

Linear System Of Equations ◽

The Matrix ◽

A Finite Group

Solving linear system of equationsAx=benters into many scientific applications. In this paper, we consider a special kind of linear systems, the matrixAis an equivariant matrix with respect to a finite group of permutations. Examples of this kind are special Toeplitz matrices, circulant matrices, and others. The equivariance property ofAmay be used to reduce the cost of computation for solving linear systems. We will show that the quadratic form is invariant with respect to a permutation matrix. This helps to know the multiplicity of eigenvalues of a matrix and yields corresponding eigenvectors at a low computational cost. Applications for such systems from the area of statistics will be presented. These include Fourier transforms on a symmetric group as part of statistical analysis of rankings in an election, spectral analysis in stationary processes, prediction of stationary processes and Yule-Walker equations and parameter estimation for autoregressive processes.

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