The integral of a symmetric unimodal function over a symmetric convex set and some probability inequalities
T. W. Anderson
- Vol. 6, Iss: 2, pp 170-176
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The article was published on 1955-02-01 and is currently open access. It has received 552 citations till now. The article focuses on the topics: Convex set & Subderivative.read more
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Optimal Bounds on the Modulus of Continuity of the Uncentered Hardy–Littlewood Maximal Function
TL;DR: In this paper, the modulus of continuity of the uncentered maximal function in terms of the given function was derived via integral formulas, and the best constants for Lipschitz and Holder functions on proper subintervals of ℝ were derived.
Journal ArticleDOI
Spectral conditions for strong local nondeterminism and exact Hausdorff measure of ranges of Gaussian random fields
Nana Luan,Yimin Xiao +1 more
TL;DR: In this paper, the exact Hausdorff measure function for Gaussian random fields with stationary increments has been derived and a sufficient condition for such a Gaussian field to be strongly locally nondeterministic has been given.
Journal ArticleDOI
Mutual Information Jammer-Relay Games
TL;DR: This work considers a two-person zero-sum mutual information game between one jammer (J) and one relay (Rfr) in both nonfading and fading scenarios and derives optimal pure or mixed strategies for J and Rfr depending on the link qualities and whether the players are active during the SrarrD channel training.
Journal ArticleDOI
Stochastic Integration of Operator-Valued Functions with Respect to Banach Space-Valued Brownian Motion
TL;DR: In this article, it was shown that almost all orbitsx are stochastically integrable with respect to a real Brownian motion if and only if they can be expressed as a linear extension of a real-Brownian motion.
Book ChapterDOI
Roth’s Orthogonal Function Method in Discrepancy Theory and Some New Connections
TL;DR: In this article, the authors give a comprehensive introduction to the circle of questions surrounding the classical problems of discrepancy theory, unified by the same approach originated in the work of Klaus Roth (Mathematika 1:73-79, 1954) and based on multiparameter Haar (or other orthogonal) function expansions.
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Asymptotic Theory of Certain "Goodness of Fit" Criteria Based on Stochastic Processes
TL;DR: In this article, a general method for calculating the limiting distributions of these criteria is developed by reducing them to corresponding problems in stochastic processes, which in turn lead to more or less classical eigenvalue and boundary value problems for special classes of differential equations.
BookDOI
Theorie der Konvexen Körper
T. Bonnesen,W. Fenchel +1 more
TL;DR: In this article, Minkowski et al. den engen Zusammenhang dieser Begriffbildungen und Satze mit der Frage nach der bestimmung konvexer Flachen durch ihre GAusssche Krtim mung aufgedeckt und tiefliegende diesbeztigliche Satze bewiesen.
Journal ArticleDOI
The Cramer-Smirnov Test in the Parametric Case
TL;DR: In this paper, the authors extended the Cramer-Smirnov and von Mises test to the parametric case, a suggestion of Cramer [1], see also [2].