A condition for the mutual absolute continuity of two Gaussian measures, corresponding to a stationary process, and the asymptotic behavior of the reproducing kernel

1990 ◽  
Vol 52 (2) ◽  
pp. 2980-2982
Author(s):  
V. N. Solev
Keyword(s):  
Asymptotic Behavior ◽  
Absolute Continuity ◽  
Reproducing Kernel ◽  
Stationary Process ◽  
Gaussian Measures

scholarly journals On a Necessary Condition for the Sample Path Continuity of Weakly Stationary Processes

1970 ◽  
Vol 38 ◽  
pp. 103-111 ◽  
Author(s):  
Izumi Kubo
Keyword(s):  
Distribution Function ◽  
Asymptotic Behavior ◽  
Spectral Distribution ◽  
Covariance Function ◽  
Stationary Process ◽  
Sufficient Conditions ◽  
Sample Path ◽  
Necessary Condition ◽  
Stationary Processes ◽  
Spectral Distribution Function

We shall discuss the sample path continuity of a stationary process assuming that the spectral distribution function F(λ) is given. Many kinds of sufficient conditions have been given in terms of the covariance function or the asymptotic behavior of the spectral distribution function.

scholarly journals ON THE UNIVERSALITY OF THE DISTRIBUTION OF THE GENERALIZED EIGENVALUES OF A PENCIL OF HANKEL RANDOM MATRICES

2013 ◽  
Vol 02 (01) ◽  
pp. 1250014 ◽  
Author(s):  
PIERO BARONE
Keyword(s):  
Asymptotic Behavior ◽  
Integral Representation ◽  
Random Matrices ◽  
Interpolation Problem ◽  
Stationary Process ◽  
Hankel Matrices ◽  
Spherical Distribution ◽  
Generalized Eigenvalues ◽  
Specific Distribution ◽  
Finite Set

Universality properties of the distribution of the generalized eigenvalues of a pencil of random Hankel matrices, arising in the solution of the exponential interpolation problem of a complex discrete stationary process, are proved under the assumption that every finite set of random variables of the process have a multivariate spherical distribution. An integral representation of the condensed density of the generalized eigenvalues is also derived. The asymptotic behavior of this function turns out to depend only on stationarity and not on the specific distribution of the process.

Absolute continuity of perturbed Gaussian measures

1998 ◽  
Vol 34 (2) ◽  
pp. 298-300
Author(s):  
V. G. Bondarenko
Keyword(s):  
Absolute Continuity ◽  
Gaussian Measures

On estimation of parameters of Gaussian stationary processes

1979 ◽  
Vol 16 (03) ◽  
pp. 575-591 ◽  
Author(s):  
Masanobu Taniguchi
Keyword(s):  
Asymptotic Behavior ◽  
Spectral Density ◽  
Stationary Process ◽  
Parametric Family ◽  
Stationary Processes ◽  
Estimation Of Parameters ◽  
Spectral Densities ◽  
Gaussian Stationary Process

In fitting a certain parametric family of spectral densities fθ (x) to a Gaussian stationary process with the true spectral density g (x), we propose two estimators of θ, say by minimizing two criteria D 1 (·), D 2(·) respectively, which measure the nearness of fθ (x) to g (x). Then we investigate some asymptotic behavior of with respect to efficiency and robustness.

scholarly journals Eigenvalue Problem for Discrete Jacobi–Sobolev Orthogonal Polynomials

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 182
Author(s):  
Juan F. Mañas-Mañas ◽  
Juan J. Moreno-Balcázar ◽  
Richard Wellman
Keyword(s):  
Asymptotic Behavior ◽  
Reproducing Kernel ◽  
Uniform Norm ◽  
Inner Product ◽  
Logarithmic Scale ◽  
Orthonormal Polynomials ◽  
Limit Value ◽  
Sobolev Orthogonal Polynomials ◽  
Kernel Hilbert Spaces ◽  
The One

In this paper, we consider a discrete Sobolev inner product involving the Jacobi weight with a twofold objective. On the one hand, since the orthonormal polynomials with respect to this inner product are eigenfunctions of a certain differential operator, we are interested in the corresponding eigenvalues, more exactly, in their asymptotic behavior. Thus, we can determine a limit value which links this asymptotic behavior and the uniform norm of the orthonormal polynomials in a logarithmic scale. This value appears in the theory of reproducing kernel Hilbert spaces. On the other hand, we tackle a more general case than the one considered in the literature previously.

On estimation of parameters of Gaussian stationary processes

1979 ◽  
Vol 16 (3) ◽  
pp. 575-591 ◽  
Author(s):  
Masanobu Taniguchi
Keyword(s):  
Asymptotic Behavior ◽  
Spectral Density ◽  
Stationary Process ◽  
Parametric Family ◽  
Stationary Processes ◽  
Estimation Of Parameters ◽  
Spectral Densities ◽  
Gaussian Stationary Process

In fitting a certain parametric family of spectral densities fθ (x) to a Gaussian stationary process with the true spectral density g (x), we propose two estimators of θ, say by minimizing two criteria D1 (·), D2(·) respectively, which measure the nearness of fθ (x) to g (x). Then we investigate some asymptotic behavior of with respect to efficiency and robustness.

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