Spectral type of a polynomial of stationary Gaussian process
B. Lučić (1986)
Matematički Vesnik
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Displaying similar documents to “Spectral Multiplicity of Certain Gaussian Processes”
Spectral type of a polynomial of stationary Gaussian process
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On the tails of the distribution of the maximum of a smooth stationary Gaussian process
Jean-Marc Azaïs, Jean-Marc Bardet, Mario Wschebor (2010)
ESAIM: Probability and Statistics
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We study the tails of the distribution of the maximum of a stationary Gaussian process on a bounded interval of the real line. Under regularity conditions including the existence of the spectral moment of order , we give an additional term for this asymptotics. This widens the application of an expansion given originally by Piterbarg [CITE] for a sufficiently small interval.
On small deviations of Gaussian processes using majorizing measures
Michel J. G. Weber (2012)
Colloquium Mathematicae
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We give two examples of periodic Gaussian processes, having entropy numbers of exactly the same order but radically different small deviations. Our construction is based on Knopp's classical result yielding existence of continuous nowhere differentiable functions, and more precisely on Loud's functions. We also obtain a general lower bound for small deviations using the majorizing measure method. We show by examples that our bound is sharp. We also apply it to Gaussian independent sequences...
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J.-R. Pycke (2006)
Banach Center Publications
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Karhunen-Loève expansions of Gaussian processes have numerous applications in Probability and Statistics. Unfortunately the set of Gaussian processes with explicitly known spectrum and eigenfunctions is narrow. An interpretation of three historical examples enables us to understand the key role of the Laplacian. This allows us to extend the set of Gaussian processes for which a very explicit Karhunen-Loève expansion can be derived.
Poincaré and log-Sobolev inequality for stationary Gaussian processes and moving average processes
Guangfei Li, Yu Miao, Huiming Peng, Liming Wu (2005)
Annales mathématiques Blaise Pascal
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For stationary Gaussian processes, we obtain the necessary and sufficient conditions for Poincaré inequality and log-Sobolev inequality of process-level and provide the sharp constants. The extension to moving average processes is also presented, as well as several concrete examples.