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Algebra of random variables: Algebra, Axiom, Probability theory, Representation theorem, Measure (mathematics), Linear functional, Free probability, Quantum probability - Tapa blanda

 
9786132742698: Algebra of random variables: Algebra, Axiom, Probability theory, Representation theorem, Measure (mathematics), Linear functional, Free probability, Quantum probability

Sinopsis

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In the algebraic axiomatization of probability theory, the primary concept is not that of probability of an event, but rather that of a random variable. Probability distributions are determined by assigning an expectation to each random variable. The measurable space and the probability measure arise from the random variables and expectations by means of well-known representation theorems of analysis. One of the important features of the algebraic approach is that apparently infinite-dimensional probability distributions are not harder to formalize than finite-dimensional ones.

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Reseña del editor

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In the algebraic axiomatization of probability theory, the primary concept is not that of probability of an event, but rather that of a random variable. Probability distributions are determined by assigning an expectation to each random variable. The measurable space and the probability measure arise from the random variables and expectations by means of well-known representation theorems of analysis. One of the important features of the algebraic approach is that apparently infinite-dimensional probability distributions are not harder to formalize than finite-dimensional ones.

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