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White noise

About: White noise is a research topic. Over the lifetime, 16496 publications have been published within this topic receiving 318633 citations.


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Journal ArticleDOI
TL;DR: New sufficient conditions that ensuring that the system model is positive recurrent are established are established, and the existence of a unique ergodic stationary distribution is shown.

100 citations

Journal ArticleDOI
TL;DR: In this article, a new spectral estimate, called the maximum entropy method, was described, which maximizes the information of a signal under the constraint that the estimated autocorrelation function of the signal is the Fourier transform of the spectral power density.
Abstract: A new spectral estimate, called the maximum entropy method, is described. This estimate was originated by John Parker Burg for use in seismic wave analysis. In the maximum entropy method the entropy, or information, of a signal is maximized under the constraint that the estimated autocorrelation function of the signal is the Fourier transform of the spectral power density. The spectral estimates are calculated in two ways: (1) by minimization of the error power to obtain the coefficients of the prediction error filter, as suggested by Burg, and (2) by a direct solution of the matrix equation using an algorithm due to Norman Levinson. For comparison a Blackman-Tukey technique, calculated with a Hamming window, is used also. We illustrate these three methods by applying them to a composite signal consisting of four sinusoids of unit amplitude: one each at high and low frequencies and two at moderate frequencies with respect to the Nyquist frequency, to which is added white noise of 0.5 amplitude. Results are shown to indicate that the best correspondence with the input spectrum is provided by the Burg technique. Applications of the maximum entropy method to geomagnetic micropulsations reveal complex multiplet structure in the Pc 4, 5 range. Such structure, not previously resolved by conventional techniques, has been predicted by a recent theory of magnetospheric resonances. In a period range 7 orders of magnitude longer than micropulsation periods, analysis of annual sunspot means shows that the 11-yr band is composed of at least three distinct lines. With each of these lines is associated a harmonic sequence. Long periods of the order of 100 yr also are revealed.

100 citations

Journal ArticleDOI
TL;DR: In this article, the Bernstein-von Mises theorems for nonparametric Bayes priors in the Gaussian white noise model are proved, and it is demonstrated how such results justify Bayes methods as efficient frequentist inference procedures in a variety of concrete non-parametric problems.
Abstract: Bernstein-von Mises theorems for nonparametric Bayes priors in the Gaussian white noise model are proved. It is demonstrated how such results justify Bayes methods as efficient frequentist inference procedures in a variety of concrete nonparametric problems. Particularly Bayesian credible sets are constructed that have asymptotically exact $1-\alpha$ frequentist coverage level and whose $L^2$-diameter shrinks at the minimax rate of convergence (within logarithmic factors) over H\"{o}lder balls. Other applications include general classes of linear and nonlinear functionals and credible bands for auto-convolutions. The assumptions cover nonconjugate product priors defined on general orthonormal bases of $L^2$ satisfying weak conditions.

100 citations

Journal ArticleDOI
TL;DR: In this paper, a stochastic Korteweg-de-vries equation on the real line was considered and the authors used function spaces similar to those introduced by Bourgain to prove well posedness results.

100 citations

Journal ArticleDOI
TL;DR: In this article, a procedure associated with nonlinear wavelet methods that provides adaptive confidence intervals around $f (x_0)$ in either a white noise model or a regression setting is presented.
Abstract: We present a procedure associated with nonlinear wavelet methods that provides adaptive confidence intervals around $f (x_0)$, in either a white noise model or a regression setting. A suitable modification in the truncation rule for wavelets allows construction of confidence intervals that achieve optimal coverage accuracy up to a logarithmic factor. The procedure does not require knowledge of the regularity of the unknown function $f$; it is also efficient for functions with a low degree of regularity.

100 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023238
2022535
2021488
2020541
2019558
2018537