THE FIVE INDEPENDENCES AS NATURAL PRODUCTS

Author:

MURAKI NAOFUMI1

Affiliation:

1. Mathematics Laboratory, Iwate Prefectural University, Takizawa, Iwate 020-0193, Japan

Abstract

Let [Formula: see text] be the class of all algebraic probability spaces. A "natural product" is, by definition, a map [Formula: see text] which is required to satisfy all the canonical axioms of Ben Ghorbal and Schürmann for "universal product" except for the commutativity axiom. We show that there exist only five natural products, namely tensor product, free product, Boolean product, monotone product and anti-monotone product. This means that, in a sense, there exist only five universal notions of stochastic independence in noncommutative probability theory.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Mathematical Physics,Statistics and Probability,Statistical and Nonlinear Physics

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