Small ball probability
Webb5.1 Quadratic small-ball probabilities. To prove Theorem 1.1 and 1.2, we need the following small-ball inequalities for quadratic forms. The derivation is almost identical to the approach in [Reference Vershynin 30, Theorem 8.1], with improvements coming from Theorem 3.7 and Proposition 3.5 (respectively Theorem 4.8). Webb23 okt. 2007 · SMALL BALL PROBABILITIES FOR GAUSSIAN RANDOM FIELDS AND TENSOR PRODUCTS OF COMPACT OPERATORS TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY Volume 360, Number 3, March 2008, Pages 1443–1474 S 0002-9947(07)04233-X Article electronically published on October 23, 2007
Small ball probability
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WebbThe small ball problem for the integrated process of a real–valued Brownian motion is solved. In sharp contrast to more standard methods, our approach relies on the sample path properties of Brownian motion together with facts about local times and Lévy processes. References Similar Articles Additional Information WebbSmall ball probabilities are estimated for Gaussian processes with stationary increments when the small balls are given by various Hölder norms. As an application we establish …
Webb22 nov. 2006 · Modern apparatuses allow us to collect samples of functional data, mainly curves but also images. On the other hand, nonparametric statistics produces useful tools for standard data exploration. This book links these two fields of modern statistics by explaining how functional data can be studied through parameter-free statistical ideas. Webb18 sep. 2015 · The solutions need to be positive integers, and the problem asks for the smallest one, so you need to experiment. Simplify the notation a bit by making M the …
Webb31 jan. 2016 · They don’t mind small rewards for their labours but they sulk if another dog gets a bigger reward for bringing back the same number of rabbits. All who have worked with animals in a spirit of sympathy agree that dogs, horses, pigs, cats, jackdaws, even geese – an ever-growing line-up of mammals and birds – are bright enough, and … WebbSmall ball probabilities have been very well studied in many different settings but most of the results in the literature are for Gaussian processes; see for an extensive survey on various developments and applications of small ball probabilities for Gaussian processes.
Webb1 mars 2007 · Small ball probabilities for S(t) are obtained under the L2-norm on [0, 1]d, and under the sup-norm on [0, 1]2 which implies Talagrand's result for the Brownian sheet.
WebbSmall ball probabilities for Gaussian measures and related inequalities and applications 8. Isoperimetry and hypercontractivity. 4 In memory of A. Ehrhard The Gaussian isoperimetric inequality, and its related concentration phenomenon, is one of the most important properties of Gaussian measures. darty mqWebbSection 2 how other approximation quantities are related to small ball probabilities. These estimates are of independent interest. Based on a totally different argument than the one used to establish (iv) of Theorem 1.1, they provide a preliminary estimate of the small ball probability in terms of metric entropy without any regularity conditions. darty nancy centrehttp://www.mcqmc2012.unsw.edu.au/slides/MCQMC2012_Aurzada.pdf darty mulhouse cataloguebiswaroop roy choudharyWebbOur proofs rely on results from small ball probability and exploit the structure of general orthogonal polynomials. Our methods also work for sequences of asymptotically minimal polynomials in Lp(τ), where p∈(0,∞]. In particular, sequences of Lp … darty msiWebbThe Annals of Probability 2003, Vol. 31, No. 2, 1052-1077 0 Institute of Mathematical Statistics, 2003 QUADRATIC FUNCTIONALS AND SMALL BALL PROBABILITIES FOR THE m-FOLD INTEGRATED BROWNIAN MOTION BY XIA CHEN1 AND WENBO V. LI2 University of Tennessee and University of Delaware Let the Gaussian process Xm(t) be the m-fold … biswaroop roy chowdhury books free downloadWebbSmall ball probability estimates for log-concave measures Grigoris Paouris Abstract We establish a small ball probability inequality for isotropic log-concave probability … biswaroop roy chowdhury arrested