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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Covariance of stochastic integrals with respect to fractional Brownian motion
Yohaï Maayan,Eddy Mayer-Wolf +1 more
TL;DR: In this article, an explicit expression for the cross-covariance between stochastic integral processes with respect to a $d$-dimensional fractional Brownian motion (fBm) with Hurst parameter (H>1/2), where the integrands are vector fields applied to $B_t, is given.
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Chung-type law of the iterated logarithm and exact moduli of continuity for a class of anisotropic Gaussian random fields
TL;DR: In this paper , a Chung-type law of the iterated logarithm and the exact local and uniform moduli of continuity for a large class of anisotropic Gaussian random fields with a harmonizable-type integral representation and the property of strong local nondeterminism were established.
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Iterative Configuration of Programmable Unitary Converter Based on Few-Layer Redundant Multiplane Light Conversion
TL;DR: In this article , a fast iterative configuration method for MPLC is proposed, following the mathematical review of the matrix distance and proposal of an alternative norm, and the authors show through numerical simulations that adding a few redundant layers significantly improves the convergence of the MPLC architecture.
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On a multivariate normal probability minimization problem
TL;DR: In this paper, it was proved that the conjecture of Shafer and Olkin (1983) is correct, and a known inequality was generalized to the case of positive definite correlation matrices.
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M-decomposability, elliptical unimodal densities, and applications to clustering and kernel density estimation
Nicholas Chia,Junji Nakano +1 more
TL;DR: It is proved that all elliptical unimodal densities are M-undecomposable, and the results show that M-decomposability can be used as a non-parametric criterion to locate modes in probability densities.
References
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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.
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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.
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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].