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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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...
Renze, John, Wagon, Stan, Wick, Brian (2001)
Experimental Mathematics
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Rovskiĭ, V.A. (2004)
Zapiski Nauchnykh Seminarov POMI
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Eisenbaum, Nathalie (2005)
Electronic Journal of Probability [electronic only]
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Slobodanka S. Mitrović (2005)
Matematički Vesnik
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Galtier, Thomas, Gupta, Sayan, Rychlik, Igor (2010)
Journal of Probability and Statistics
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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.
M. Clausel, F. Roueff, M. S. Taqqu, C. Tudor (2014)
ESAIM: Probability and Statistics
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We consider stationary processes with long memory which are non-Gaussian and represented as Hermite polynomials of a Gaussian process. We focus on the corresponding wavelet coefficients and study the asymptotic behavior of the sum of their squares since this sum is often used for estimating the long–memory parameter. We show that the limit is not Gaussian but can be expressed using the non-Gaussian Rosenblatt process defined as a Wiener–Itô integral of order 2. This happens even if the...
Nathan Keller, Elchanan Mossel, Arnab Sen (2014)
Annales de l'I.H.P. Probabilités et statistiques
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In a recent paper, we presented a new definition of influences in product spaces of continuous distributions, and showed that analogues of the most fundamental results on discrete influences, such as the KKL theorem, hold for the new definition in Gaussian space. In this paper we prove Gaussian analogues of two of the central applications of influences: Talagrand’s lower bound on the correlation of increasing subsets of the discrete cube, and the Benjamini–Kalai–Schramm (BKS) noise sensitivity...
Manfred G. Madritsch (2008)
Acta Arithmetica
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Michel Talagrand (1988)
Annales de l'I.H.P. Probabilités et statistiques
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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.
Mohamedou Ould Haye (2002)
ESAIM: Probability and Statistics
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We study the asymptotic behavior of the empirical process when the underlying data are gaussian and exhibit seasonal long-memory. We prove that the limiting process can be quite different from the limit obtained in the case of regular long-memory. However, in both cases, the limiting process is degenerated. We apply our results to von–Mises functionals and -Statistics.