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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Book ChapterDOI
Exit Times of Brownian Motion, Harmonic Majorization, and Hardy Spaces
Burgess Davis,Renming Song +1 more
TL;DR: In this paper, the first time a Brownian motion in R n starts at a point x in R, and ends at X's departure from R n is described as follows: \tau \left( \omega \right) = \inf \left\{ {t > 0:{X_t}(\omega)
otin R} \right\}.
Journal ArticleDOI
Sparsity-promoting and edge-preserving maximum a posteriori estimators in non-parametric Bayesian inverse problems
TL;DR: The results are remarkable for two reasons: first, the prior distribution is non-Gaussian and does not meet the smoothness conditions required in previous research on non-parametric MAP estimates, which analytically justifies existing uses of the MAP estimate in finite but high dimensional discretizations of Bayesian inverse problems with the considered Besov priors.
Journal ArticleDOI
The Brunn-Minkowski inequality for random sets
TL;DR: In this article, a generalization of the Brunn-Minkowski inequality in terms of random sets is presented, which provides a natural proof of Mudholkar's generalized Anderson-type inequality.
Correlated Jamming in Multiple Access Channels 1
S. Shafiee,Sennur Ulukus +1 more
TL;DR: This work investigates the behavior of two users and one jammer in an AWGN channel with and without fading when they participate in a zero-sum mutual information game with the sum capacity as the objective function.
References
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Journal ArticleDOI
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].