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Quantum Probability Theory [PDF]
Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, 2005 The mathematics of classical probability theory was subsumed into classical measure theory by Kolmogorov in 1933. Quantum theory as nonclassical probability theory was incorporated into the beginnings of noncommutative measure theory by von Neumann in ...
Redei, Miklos, Summers, Stephen J.
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An inequality in probability theory [PDF]
Proceedings of the American Mathematical Society, 1955 1. Let x and y be random variables with finite expectations. We shall say that x dominates y if e I{(x) } > E {+(y) } whenever q5 is a continuous convex function on the real line R1. (The expectations ?{+(x) } and ?{+(y) } are always well defined if + oo is admitted as a value.) Assume now that xi and x2 are independent and dominate respectively the ...
G. A. Hunt
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A noncommutative probability theory [PDF]
Transactions of the American Mathematical Society, 1978 A noncommutative probability theory is developed in which no boundedness, finiteness, or “tracial” conditions are imposed. The underlying structure of the theory is a “probability algebra” ( a , ω ) (\mathcal {a},\omega ) where a \mathcal {a} is a ...
Stanley Gudder, R. L. Hudson
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Problems in Probability Theory [PDF]
The Annals of Mathematical Statistics, 1947 Harald Cramér
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Conditioning in tropical probability theory [PDF]
, 2019 We define a natural operation of conditioning of tropical diagrams of probability spaces and show that it is Lipschitz continuous with respect to the asymptotic entropy distance.Comment: 12 pages, V2 - updated ...
Matveev, Rostislav +1 more
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Constructor theory of probability [PDF]
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2016 Unitary quantum theory, having no Born Rule, is non-probabilistic . Hence the notorious problem of reconciling it with the unpredictability and appearance of stochasticity in quantum measurements.
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The splitting process in free probability theory [PDF]
, 2015 Free cumulants were introduced by Speicher as a proper analog of classical cumulants in Voiculescu's theory of free probability. The relation between free moments and free cumulants is usually described in terms of Moebius calculus over the lattice of ...
Ebrahimi-Fard, Kurusch, Patras, Frederic
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Harold Jeffreys's Theory of Probability Revisited
, 2009 Published exactly seventy years ago, Jeffreys's Theory of Probability (1939) has had a unique impact on the Bayesian community and is now considered to be one of the main classics in Bayesian Statistics as well as the initiator of the objective Bayes ...
Bernardo, J. M. +8 more
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