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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Chung’s law of the iterated logarithm for anisotropic Gaussian random fields
Nana Luan,Yimin Xiao +1 more
TL;DR: In this paper, the authors established Chung's law of the iterated logarithm for a class of anisotropic Gaussian random fields with stationary increments, which is applicable to space-time Gaussian Random Fields and solution to the stochastic fractional heat equation.
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Connecting pairwise geodesic spheres by depth: DCOPS
TL;DR: The classical notion of spherical depth for data in Rk is extended to the case of data on a Riemannian manifold and it is shown that this notion has several desirable properties.
Book ChapterDOI
Pricing of Volume-Weighted Average Options: Analytical Approximations and Numerical Results
TL;DR: In this article, the volume weighted average price (VWAP) is used as a benchmark price by market participants and can be regarded as an estimate for the price that a passive trader will pay to purchase securities in a market.
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Lower Error Bounds for Strong Approximation of Scalar SDEs with non-Lipschitzian Coefficients
TL;DR: In this article, the authors studied pathwise approximation of scalar stochastic differential equations at a single time point or globally in time by means of methods that are based on finitely many observations of the driving Brownian motion.
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Ordering of Multivariate Risk Models with Respect to Extreme Portfolio Losses
TL;DR: In this article, an ordering called asymptotic portfolio loss ordering (apl) is introduced which is closely connected with the extremal risk index and which allows to compare different stochastic models of risk vectors w.r.t.
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.
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.
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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].