The Gaussian zoo.
Renze, John, Wagon, Stan, Wick, Brian (2001)
Experimental Mathematics
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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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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...
Xu Sun, Jinqiao Duan, Xiaofan Li, Xiangjun Wang (2015)
Banach Center Publications
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The Kalman filter is extensively used for state estimation for linear systems under Gaussian noise. When non-Gaussian Lévy noise is present, the conventional Kalman filter may fail to be effective due to the fact that the non-Gaussian Lévy noise may have infinite variance. A modified Kalman filter for linear systems with non-Gaussian Lévy noise is devised. It works effectively with reasonable computational cost. Simulation results are presented to illustrate this non-Gaussian filtering...
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.
Manfred G. Madritsch (2008)
Acta Arithmetica
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Tomás Cipra, Asunción Rubio (1991)
Trabajos de Estadística
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The dynamic linear model with a non-linear non-Gaussian observation relation is considered in this paper. Masreliez's theorem (see Masreliez's (1975)) of approximate non-Gaussian filtering with linear state and observation relations is extended to the case of a non-linear observation relation that can be approximated by a second-order Taylor expansion.
Nicolas Privault, Anthony Réveillac (2012)
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.
Pathmanabhan, A., Dinesh, S. (2007)
Discrete Dynamics in Nature and Society
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Yuichi Futa, Hiroyuki Okazaki, Daichi Mizushima, Yasunari Shidama (2013)
Formalized Mathematics
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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. ...
Elliot H. Lieb (1990)
Inventiones mathematicae
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Ermakov, M.S. (2004)
Zapiski Nauchnykh Seminarov POMI
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Papanikolaou, V., Plataniotis, K. N., Venetsanopoulos, A. N. (1999)
Mathematical Problems in Engineering
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M. Talagrand (1993)
Geometric and functional analysis
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Kumar, Rajendra (2006)
Journal of Applied Mathematics and Decision Sciences
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