For an integer b > 1 let (phi(b)(n))(n >= 0) denote the base b van der Corput sequence in [0, 1). Answering a question of O. Strauch, C. Aisleitner and M. Hofer showed that the distribution function of (phi(b)(n...
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For an integer b > 1 let (phi(b)(n))(n >= 0) denote the base b van der Corput sequence in [0, 1). Answering a question of O. Strauch, C. Aisleitner and M. Hofer showed that the distribution function of (phi(b)(n), phi(b)(n + 1),..., phi(b)(n + s - 1))(n >= 0) on [0, 1)(s) exists and is a copula. In this note we show that this phenomenon extends to a broad class of subsequences of the van der Corput sequences. (C) 2013 Royal Dutch Mathematical Society (KWG). Published by Elsevier B.V. All rights reserved.
Encouraged by the study of extremal limits for sums of the form lim(N ->) (infinity) 1/N Sigma(N)(n=1) c(x(n), y(n)) with uniformly distributed sequences {x(n)}, {y(n)} the following extremal problem is of interest...
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Encouraged by the study of extremal limits for sums of the form lim(N ->) (infinity) 1/N Sigma(N)(n=1) c(x(n), y(n)) with uniformly distributed sequences {x(n)}, {y(n)} the following extremal problem is of interest max(gamma) integral([0,1]2) c(x, y) gamma (dx, dy), for probability measures gamma on the unit square with uniform marginals, i.e., measures whose distribution function is a copula. The aim of this article is to relate this problem to combinatorial optimization and to the theory of optimal transport. Using different characterizations of maximizing gamma's one can give alternative proofs of some results from the field of uniform distribution theory and beyond that treat additional questions. Finally, some applications to mathematical finance are addressed. (C) 2015 Royal Dutch Mathematical Society (KWG). Published by Elsevier B.V. All rights reserved.
For continuous random vectors X = (X-1,X-2,...,X-n) and multivariate distribution functions H-1 and H-2 with common univariate marginals, we study the distribution function of the random variable H-1(X) given that the...
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For continuous random vectors X = (X-1,X-2,...,X-n) and multivariate distribution functions H-1 and H-2 with common univariate marginals, we study the distribution function of the random variable H-1(X) given that the joint distribution function of X is H-2. We show that the distribution function of H-1(X) depends only on the copulas C-1 and C-2 associated with H-1 and H-2, and examine various properties of these distribution functions. We also illustrate some applications including multivariate dependence orderings. (C) 2003 Elsevier B.V. All rights reserved.
We discuss a two-dimensional analog of the probability integral transform for bivariate distribution functions H-1 and H-2, i.e., the distribution function of the random variable H-1(X, Y) given that the joint distrib...
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We discuss a two-dimensional analog of the probability integral transform for bivariate distribution functions H-1 and H-2, i.e., the distribution function of the random variable H-1(X, Y) given that the joint distribution function of the random variables X and Y is H-2. We study the case when H-1 and H-2 have the same continuous marginal distributions, showing that the distribution function of HI(X, Y) depends only on the copulas C-1 and C-2 associated with H-1 and H-2. We examine various propel-tics of these "distribution functions of copulas", and illustrate applications including dependence orderings and measures of association. (C) 2001 Elsevier Science B.V. All rights reserved.
Algorithms involving ranking are used to suppress noise induced in IR detectors by gamma radiation, based on enhanced response to gamma photons relative to other excitation. An analytic expression for the characterist...
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A non-probabilistic interpretation of the distribution functions is obtained. The cases of instantaneous and retarded interactions are considered. The derivation is based on the use smoothing operator that does not ch...
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The previous works on whistler waves with electron temperature anisotropy narrated the dependence on plasma parameters, however, they did not explore the reasons behind the observed differences. A comparative analysis...
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The previous works on whistler waves with electron temperature anisotropy narrated the dependence on plasma parameters, however, they did not explore the reasons behind the observed differences. A comparative analysis of the whistler waves with different electron distributions has not been made to date. This paper attempts to address both these issues in detail by making a detailed comparison of the dispersion relations and growth rates of whistler waves with electron temperature anisotropy for Maxwellian, Cairns, kappa and generalized (r, q) distributions by varying the key plasma parameters for the problem under consideration. It has been found that the growth rate of whistler instability is maximum for flat-topped distribution whereas it is minimum for the Maxwellian distribution. This work not only summarizes and complements the previous work done on the whistler waves with electron temperature anisotropy but also provides a general framework to understand the linear propagation of whistler waves with electron temperature anisotropy that is applicable in all regions of space plasmas where the satellite missions have indicated their presence. (C) 2018 Author(s).
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