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QUANTIZATION OF INFORMATION THEORY (Mathematical Studies on Independence and Dependence Structure : Algebra meets Probability)openaire
On Independence of Events in Noncommutative Probability Theory [PDF]
Lobachevskii Journal of Mathematics, 2021 Abstract: We consider a tracial state ϕ on a von Neumann algebra A and assume that projections P, Q of A are independent if ϕ(PQ) = ϕ(P)ϕ(Q). First we present the general criterion of a projection pair independence. We then give a geometric criterion for independence of different pairs of projections.
А. М. Бикчентаев +1 more
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Qualitative independence in probability theory [PDF]
Theory and Decision, 1978 Probability theory is measure theory specialized by assumptions having to do with stochastic independence. Delete from probability and statistics those theorems that explicitly or implicitly (e.g., by postulating a random sample) invoke independence, and relatively little remains.
R. Duncan Luce, Louis Narens
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Stochastic independence in non-commutative probability theory
Mathematical Proceedings of the Cambridge Philosophical Society, 1979 AbstractFor a family {Xα} of random variables over a probability space , stochastic independence can be formulated in terms of factorization properties of characteristic functions. This idea is reformulated for a family {Aα} of selfadjoint operators over a probability gage space and is shown to be inappropriate as a non-commutative generalization ...
W. Driessler, Ivan F. Wilde
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Conditional independence in probability theory on MV-algebras
Soft Computing, 2003 The author considers a weakly \(\sigma\)-distributive MV-algebra \(M\) and a state on \(M\). He defines the conditional independence of two observables \(x_1\), \(x_2\) given an observable \(x_3\), and he shows that the notion has properties that are analogous to the independence in the Kolmogorov theory.
Tomáš Kroupa
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Statistical Independence in Probability, Analysis and Number Theory.
The American Mathematical Monthly, 1960 Charles H. Kraft, Mark Kac
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Probability Theory: Independence, Interchangeability, Martingales (Yuan Shih Chow and Henry Teicher)
SIAM Review, 1980 Stephen M. Samuels
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Statistical Independence in Probability, Analysis, and Number Theory
, 1959 Mark Kac
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Statistical Independence and Kolmogorov’s Probability Theory
, 1998 Independently repeated experiments with random outcomes have a formal counter-part in the mathematical concept of statistical independence. The cleanest way to introduce the latter can be found within the framework of Kolmogorov’s axiomatic probability theory which, since the 1930s, became the standard, and by far most widespread, mathematical model of
Manfred Denker +2 more
openalex +3 more sources