Contests in Higher Mathematics
Miklós Schweitzer Competitions 1962–1991
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Article
Calibrating Dependence Between Random Elements
Attempts to quantify dependence between random elements X and Y via maximal correlation go back to Gebelein (Z Angew Math Mech 21:364–379, 1941) and Rényi (Acta Math Acad Sci 10:441–451, 1959). After summarizing ...
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Article
Comments on: Tests for multivariate normality—a critical review with emphasis on weighted \(L^{2}\) -statistics
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Article
Four simple axioms of dependence measures
Recently new methods for measuring and testing dependence have appeared in the literature. One way to evaluate and compare these measures with each other and with classical ones is to consider what are reasona...
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Chapter and Conference Paper
Partial Distance Correlation
Partial distance correlation measures association between two random vectors with respect to a third random vector, analogous to, but more general than (linear) partial correlation. Distance correlation charac...
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Article
Schur properties of convolutions of gamma random variables
Sufficient conditions for comparing the convolutions of heterogeneous gamma random variables in terms of the usual stochastic order are established. Such comparisons are characterized by the Schur convexity pr...
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Article
Integer valued means
In this paper, starting with the work of Kolmogorov on continuous means, we define the four properties, Symmetry, Internality, Monotonicity, and Associativity that a discrete mean should satisfy. An extremal m...
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Article
Definetti’s Theorem for Abstract Finite Exchangeable Sequences
We show that a finite collection of exchangeable random variables on an arbitrary measurable space is a signed mixture of i.i.d. random variables. Two applications of this idea are examined, one concerning Bay...
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Chapter
Mathematics physics
In science, the countries of Austria and Hungary have probably made their nnost outstanding achievements in the areas of mathematics and logic. This includes the mathematical foundation of information technolo...
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Article
Extremal probabilities for Gaussian quadratic forms
Denote by Q an arbitrary positive semidefinite quadratic form in centered Gaussian random variables such that E(Q)=1. We prove that for an arbitrary x>0, inf Q P(Q≤x)=P(χ2 ...
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Book
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Chapter
Results of the Contests
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Chapter
Problems of the Contests
The letter in parentheses after the text of a problem refers to the section in Chapter 3 containing its solution. The topics include these areas of mathematics:
A: Algebra
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Chapter
Solutions to the Problems
Problem A.1. Determine the roots of unity in the field of p-adic numbers.
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Article
Lattice-ordered groups with a prescribed minimum for given elements
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Article
The Choquet-Deny convolution equation μ=μ*σ for probability measures on Abelian semigroups
In this note, we characterize the regular probability measures μ satisfying the Choquet-Deny convolution equation μ=μ*σ on Abelian topological semigroups for a given probability measure σ.
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Article
Eugene Lukacs, 1906–1987
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Article
Convolution quotients of nonnegative functions
LetG be a locally compact commutative Hausdorff group andf a function belonging toL 1(G). If the integral off with respect to the Haar measure is positive, then one can find a nonnegative (not identically 0) func...
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Article
A limit theorem for elementary symmetric polynomials of independent random variables
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Chapter and Conference Paper
Extensions of Partial Homomorphisms in Probability Theory
Two years ago in Amsterdam when trying to solve a problem about invariant measures on semigroups A.A.Balkema and myself arrived to the following very simple question: Are there continuous nontrivial homomorphi...
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Chapter
The Brownian Taboo Bridge with an Application in the Theory of Nonparametric Statistics
The notion of Markov chain with taboo states turned out to be a very interesting one [1], In this paper we discuss some properties of the most fundamental Markov processes (the Wiener process and the Brownian ...
