A note on almost sure central limit theorem in the joint version for the maxima and sums.
Zang, Qing-Pei, Wang, Zhi-Xiang, Fu, Ke-Ang (2010)
Journal of Inequalities and Applications [electronic only]
Similarity:
Zang, Qing-Pei, Wang, Zhi-Xiang, Fu, Ke-Ang (2010)
Journal of Inequalities and Applications [electronic only]
Similarity:
Renze, John, Wagon, Stan, Wick, Brian (2001)
Experimental Mathematics
Similarity:
Nicolas Privault, Anthony Réveillac (2011)
ESAIM: Probability and Statistics
Similarity:
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.
Rovskiĭ, V.A. (2004)
Zapiski Nauchnykh Seminarov POMI
Similarity:
Jean-Marc Azaïs, Jean-Marc Bardet, Mario Wschebor (2010)
ESAIM: Probability and Statistics
Similarity:
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.
Manfred G. Madritsch (2008)
Acta Arithmetica
Similarity:
Waclaw Timoszyk (1974)
Colloquium Mathematicae
Similarity:
J.-R. Pycke (2006)
Banach Center Publications
Similarity:
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.
Mohamedou Ould Haye (2002)
ESAIM: Probability and Statistics
Similarity:
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.
Nathan Keller, Elchanan Mossel, Arnab Sen (2014)
Annales de l'I.H.P. Probabilités et statistiques
Similarity:
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...
Nicolas Privault, Anthony Réveillac (2012)
ESAIM: Probability and Statistics
Similarity:
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.
Michel J. G. Weber (2012)
Colloquium Mathematicae
Similarity:
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...
Elchanan Mossel, Joe Neeman (2015)
Journal of the European Mathematical Society
Similarity:
We prove that under the Gaussian measure, half-spaces are uniquely the most noise stable sets. We also prove a quantitative version of uniqueness, showing that a set which is almost optimally noise stable must be close to a half-space. This extends a theorem of Borell, who proved the same result but without uniqueness, and it also answers a question of Ledoux, who asked whether it was possible to prove Borell’s theorem using a direct semigroup argument. Our quantitative uniqueness result...
Yuichi Futa, Hiroyuki Okazaki, Daichi Mizushima, Yasunari Shidama (2013)
Formalized Mathematics
Similarity:
Gaussian integer is one of basic algebraic integers. In this article we formalize some definitions about Gaussian integers [27]. We also formalize ring (called Gaussian integer ring), Z-module and Z-algebra generated by Gaussian integer mentioned above. Moreover, we formalize some definitions about Gaussian rational numbers and Gaussian rational number field. Then we prove that the Gaussian rational number field and a quotient field of the Gaussian integer ring are isomorphic. ...
Fradon, M., Heinrich, P. (2002)
Mathematical Physics Electronic Journal [electronic only]
Similarity: