A characterization of Gaussian processes that are Markovian
Waclaw Timoszyk (1974)
Colloquium Mathematicae
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Waclaw Timoszyk (1974)
Colloquium Mathematicae
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Jacques Istas (1992)
Annales de l'I.H.P. Probabilités et statistiques
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Calogero, A. (2003)
Rendiconti del Seminario Matematico
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Nicolas Privault, Anthony Réveillac (2011)
ESAIM: Probability and Statistics
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Using integration by parts on Gaussian space we construct a Stein Unbiased Risk Estimator (SURE) for the drift of Gaussian processes, based on their local and occupation times. By almost-sure minimization of the SURE risk of shrinkage estimators we derive an estimation and de-noising procedure for an input signal perturbed by a continuous-time Gaussian noise.
Eisenbaum, Nathalie (2005)
Electronic Journal of Probability [electronic only]
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B. Lučić (1986)
Matematički Vesnik
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Charles-Antoine Guérin (2000)
The journal of Fourier analysis and applications [[Elektronische Ressource]]
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Slobodanka S. Mitrović (2005)
Matematički Vesnik
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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...
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.
Van Zanten, Harry (2008)
Electronic Communications in Probability [electronic only]
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A. Cassim, Zoran Ivković (1994)
Publications de l'Institut Mathématique
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